2006 lines
470 KiB
Plaintext
2006 lines
470 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 1 动手学概率"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 1.1 随机现象与概率"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* 随机现象：在一定条件下,并不总是出现相同结果的现象。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* 随机试验：很多随机现象是可以大量重复的，如抛一枚硬币可以无限次重复，不同麦穗上的麦粒数可以大量观察等，这种可重复的随机现象又称为随机试验，简称试验。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* 随机事件：随机现象的某些基本结果组成的集合称为随机事件，简称事件,常用大写字母（如$A、B、C$）表示。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* 事件间的关系与事件的运算，设实验$E$的样本空间为$S$，而$A、B、A_{k}, (k=1,2, \\cdots)$是$S$的子集。\n",
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" * 1. 若 $A \\subset B$，则称事件$B$包含事件$A$。若$A\\subset B 且 B\\subset A$, 则 $A = B$。\n",
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" * 2. 事件$A\\cup B = \\{x| x\\in A 或x \\in B\\}$称为 事件$A$和事件$B$的**和事件**。\n",
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" * 3. 事件$A \\cap B = \\{x| x\\in A 且x \\in B\\}$称为 事件$A$和事件$B$的**积事件**。\n",
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" * 4. 事件$A - B = \\{x| x\\in A 且x \\notin B\\}$称为 事件$A$和事件$B$的**差事件**。\n",
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" * 5. 若$A \\cap B = \\varnothing$，则称事件$A$与事件$B$**互不相容（或互斥）**。\n",
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" * 6. 若$A \\cup B = S$，则称事件$A$与事件$B$**互为逆事件（对立事件）**。\n",
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" * 7. 交换律：$A\\cup B = B\\cup A, A\\cap B = B \\cap A$。\n",
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" * 8. 结合律：$A \\cup (B \\cup C) = (A \\cup B) \\cup C, A \\cap (B \\cap C) = (A \\cap B) \\cap C$。\n",
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" * 9. 分配律: $A\\cup (B \\cap C) = (A \\cup B)\\cap (A \\cup C), A\\cap (B \\cup C) = (A \\cap B)\\cup (A \\cap C)$。\n",
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" * 10. 德摩根律：$\\overline{A\\cup B}=\\bar{A}\\cap \\bar{B}, \\overline{A\\cap B}=\\bar{A}\\cup \\bar{B}$。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* 事件的概率：表示事件发生的可能性。\n",
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"> 事件的概率$P(\\cdot)$满足的条件：\n",
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"> - 1. 非负性：对于每一个事件$A, P(A) \\ge 0$。\n",
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"> - 2. 规范性：对于必然事件$S, P(S) = 1$。\n",
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"> - 3. 可列可加性：设$A_{1}, A_{2}, \\cdots, A_{k}$是两两不相容的事件，即$A_{i}A_{j}=\\varnothing, i\\ne j, i,j = 1,2, \\cdots, k.$，有$$P(A_{1}\\cup A_{2}\\cup \\cdots \\cup A_{k}) = P(A_{1})+P(A_{2})+\\cdots +P(A_{k})$$。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* 事件的独立性：若事件$A$和事件$B$满足 $P(AB)=P(A)P(B)$，则称事件$A$和事件$B$相互独立。\n",
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"> - 定理一：设$A, B$是两事件，且$P(A) > 0$，若$A, B$相互独立，则$P(B|A) =P(B)$，反之亦然（$P(A|B) = P(A)$）。\n",
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"> - 定理二：若事件$A, B$相互独立，则下列各对事件也相互独立：$$A与\\bar{B}, \\bar{A}与B, \\bar{A}与\\bar{B}$$ "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"python代码（模拟频率近似概率）"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline\n",
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"plt.style.use(\"ggplot\")\n",
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"import warnings\n",
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"warnings.filterwarnings(\"ignore\")\n",
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"plt.rcParams['font.sans-serif'] = ['SimHei', 'Songti SC', 'STFangsong']\n",
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"plt.rcParams['axes.unicode_minus'] = False\n",
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"import seaborn as sns\n",
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"import random"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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",
|
||
"text/plain": [
|
||
"<Figure size 720x432 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x432 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x432 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x432 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"def simulat_coin(test_num):\n",
|
||
" random.seed(100)\n",
|
||
" coin_list = [1 if random.random() >= 0.5 else 0 for i in range(test_num)]\n",
|
||
" coin_frequence = np.cumsum(coin_list) / (np.arange(len(coin_list)) + 1)\n",
|
||
" plt.figure(figsize=(10, 6))\n",
|
||
" plt.plot(np.arange(len(coin_list)) + 1, coin_frequence, c='blue', alpha=0.7)\n",
|
||
" plt.axhline(0.5, linestyle='--', c='red', alpha=0.5)\n",
|
||
" plt.xlabel('test_index')\n",
|
||
" plt.ylabel('frequence')\n",
|
||
" plt.title(f\"{str(test_num)} times\")\n",
|
||
" plt.show()\n",
|
||
"\n",
|
||
"simulat_coin(500)\n",
|
||
"simulat_coin(1000)\n",
|
||
"simulat_coin(5000)\n",
|
||
"simulat_coin(10000)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.2 条件概率、乘法公式、全概率公式与贝叶斯公式"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 条件概率：考虑的是事件$A$已发生的条件下事件$B$发生的概率，记为 $P(B|A)$。条件概率的计算公式为：\n",
|
||
"$$P(B|A) = \\frac{P(AB)}{P(A)}$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 条件概率$P(\\cdot|A)$也满足概率定义的三个条件：\n",
|
||
"> - 1. 非负性：对于每一个事件$B$，有$P(B|A) \\ge 0$。\n",
|
||
"> - 2. 规范性：对于必然事件$S$，有$P(S|A) = 1$。\n",
|
||
"> - 3. 可列可加性：设$B_{1}, B_{2}, \\cdots, B_{k}$是两两不相容事件，则有：$$P(B_{1}\\cup B_{2} \\cup \\cdots \\cup B_{k}|A) = P(B_{1}|A) + P(B_{2}|A) + \\cdots + P(B_{k}|A)$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 乘法公式（定理）：设$P(A)> 0$，由条件概率的计算公式可推得：\n",
|
||
"$$P(AB) = P(B|A)P(A)$$\n",
|
||
"> 推广到多个事件的积事件的情况：\n",
|
||
"> - $P(ABC) = P(C|AB)P(B|A)P(A)$\n",
|
||
"> - $P(A_{1}A_{2}\\cdots A_{n}) = P(A_{n}|A{1}\\cdots A_{n-1})P(A_{n-1}|A_{1}\\cdots A_{n-2})\\cdots P(A_{2}|A{1})P(A_{1})$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 全概率公式：设实验$E$的样本空间为$S$，$A$为$E$的事件，$B_{1}, B{2}, \\cdots, B_{n}$为$S$的一个划分，且$P(B_{i}) > 0 (i=1, 2, \\cdots, n)$，则\n",
|
||
"\\begin{aligned}\n",
|
||
"P(A) &= P(AB_{1}) + P(AB_{2}) + \\cdots + P(AB_{n}) \\\\\n",
|
||
"&= P(A|B_{1})P(B_{1}) + P(A|B_{2})P(B_{2}) + \\cdots + P(A|B_{n})P(B_{n})\n",
|
||
"\\end{aligned}"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 贝叶斯公式：设实验$E$的样本空间为$S$，$A$为$E$的事件，$B_{1}, B_{2}, \\cdots, B_{n}$为$S$的一个划分，且$P(A)>0, P(B_{i})>0 (i=1,2, \\cdots, n)$，则\n",
|
||
"\\begin{aligned}\n",
|
||
"P(B_{i}|A) = \\frac{P(AB_{i})}{P(A)} \n",
|
||
"= \\frac {P(A|B_{i})P(B_{i})}{P(A|B_{1})P(B_{1})+P(A|B_{2})P(B_{2})+ \\cdots P(A|B_{n})P(B_{n})}\n",
|
||
"\\end{aligned}"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"##### **三门问题**(例子)：是一个源自博弈论的数学游戏问题, 大致出自美国的 电视游戏节目 Let's Make a Deal。问题的名字来自该节目的主持人蒙提・霍尔 (Monty Hall)。这个游戏的玩法是：参赛者会看见三扇关闭了的门，其中一扇的后面有一辆汽车，选中后面有车的那扇门就可以赢得该汽车, 而另外两扇门后面则各藏有一只山羊。当参赛者选定了一扇门，但未去开启它的时候，节目主持人会开启剩下两扇门的其中一扇, 露出其中一只山羊。主持人其后会问参赛者要不要换另一扇仍然关上的门。问题是：换另一扇门会否增加参赛者赢得汽车的机会率？"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"分析：设$A_{i} (i = 1, 2, 3)$表示第$i$扇门及门后为山羊，$\\bar{A_{i}}$表示第$i$扇门及门后为汽车。\n",
|
||
"\n",
|
||
"1. 参赛者不改变决策时，则结果和主持人没有关系，只与参赛者与门后面的物品有关，参赛者选中门$i$为汽车的概率为：\n",
|
||
"<style>\n",
|
||
"table\n",
|
||
"{\n",
|
||
" margin: auto;\n",
|
||
"}\n",
|
||
"</style>\n",
|
||
"\n",
|
||
"|门1（车）|门2（羊）|门3（羊）|\n",
|
||
"|:---:|:---:|:---:|\n",
|
||
"\n",
|
||
"$$P(car) = \\frac{1}{3}$$\n",
|
||
"\n",
|
||
"2. 参赛者改变决策时，可能的情况为：\n",
|
||
"<style>\n",
|
||
"table\n",
|
||
"{\n",
|
||
" margin: auto;\n",
|
||
"}\n",
|
||
"</style>\n",
|
||
"\n",
|
||
"|门1（车）|门2（羊）|门3（羊）|\n",
|
||
"|:---:|:---:|:---:|\n",
|
||
"|选|开|换|\n",
|
||
"|换|选|开|\n",
|
||
"|换|开|选|\n",
|
||
"\n",
|
||
"$$P(car) = \\frac{2}{3}$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（模拟三门问题）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"参赛者不改变决策获得汽车的概率：33.35 %\n",
|
||
"参赛者改变决策获得汽车的概率：66.64999999999999 %\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import random \n",
|
||
"\n",
|
||
"class Montyhall():\n",
|
||
" def __init__(self, test_num):\n",
|
||
" self.test_num = test_num\n",
|
||
" self.no_change = 0 # 记录未换门获得汽车的次数\n",
|
||
" self.change = 0 # 记录换门后获得汽车的次数\n",
|
||
" def start(self):\n",
|
||
" door_list = [1, 2, 3]\n",
|
||
" for i in range(self.test_num):\n",
|
||
" choice = random.choice(door_list) # 参赛者随机选一个门\n",
|
||
" car = random.choice(door_list) # 随机假定一个门后是汽车\n",
|
||
" if choice == car :\n",
|
||
" self.no_change += 1 # 参赛者选中的门后恰是汽车，不改变即获得汽车\n",
|
||
" else:\n",
|
||
" self.change += 1 # 参赛者选中的门后不是汽车，主持人打开另一扇是山羊的门，参赛者则换门后获得汽车\n",
|
||
" print(\"参赛者不改变决策获得汽车的概率：{}\".format((self.no_change/self.test_num)*100), '%')\n",
|
||
" print(\"参赛者改变决策获得汽车的概率：{}\".format((self.change/self.test_num)*100), '%')\n",
|
||
" \n",
|
||
"montyhall = Montyhall(10000)\n",
|
||
"montyhall.start()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.3 一维随机变量及其分布函数和密度函数"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 随机变量：取值带有随机性的变量$\\bf{X}$称为随机变量。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 离散型随机变量：随机变量$\\bf{X}$的取值是有限个或可列无限多个，这种变量称为**离散型随机变量**。\n",
|
||
"> 三种重要的离散型随机变量及其分布律：\n",
|
||
"> - 1. $(0 - 1)$分布：随机变量$\\bf{X}$的取值为 0 或 1，分布律为：$$P\\{{\\bf{X}}=k\\}=p^{k}(1-p)^{1-k}, k = 0, 1 (0 < p < 1)$$\n",
|
||
"> - 2. 二项分布：设实验$E$只有可能两个结果：$A, \\bar{A}$，则称$E$为伯努利实验。设$P(A)=p (0< p < 1)$，此时$P(\\bar{A}) = 1-p$，将$E$独立重复地进行$n$次，则称为$n$重伯努利实验。$n$重伯努利实验服从二项分布，分布律为：$$P\\{{\\bf{X}}=k\\}=C_{n}^{k}p^{k}(1-p)^{n-k}, k =1, 2, \\cdots, n$$ $\\bf{X}$表示实验中$A$发生的次数。\n",
|
||
"> - 3. 泊松分布：设随机变量所有可能的取值为$0, 1, 2, \\cdots$，而取各个值的概率为：$$P\\{{\\bf{X}}=k\\} = \\frac{\\lambda ^{k} e^{-\\lambda}}{k!}, k= 0, 1, 2, \\cdots, $$ 其中$\\lambda > 0$是常数，则称$\\bf{X}$服从参数为$\\lambda$的泊松分布，记为$\\bf{X} \\sim \\pi (\\lambda)$ \n",
|
||
"泊松定理：设$\\lambda > 0$是一个常数，$n$是任意正整数，设$np_{n}=\\lambda$，则对一任意固定的非负整数$k$，有 $$\\lim_{n \\to \\infty}C_{n}^{k}p_{n}^{k}(1-p_{n})^{n-k}= \\frac{\\lambda ^{k} e^{-\\lambda}}{k!}$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 随机变量$\\bf{X}$的分布函数$F$：设$\\bf{X}$是一个随机变量，$x$是任意实数，函数$$F(x)=P\\{{\\bf{X}} \\le x\\}, -\\infty < x < \\infty$$ 称为$\\bf{X}$的分布函数。 \n",
|
||
"对于任意的实数$x_{1}, x_{2}$，有：$P\\{x_{1} < {\\bf{X}} \\le x_{2} \\} = P\\{{\\bf{X}} \\le x_{2}\\} -P\\{{\\bf{X}} \\le x_{1}\\} = F(x_{2}) - F(x_{1})$。\n",
|
||
"> 分布函数$F(x)$的基本性质：\n",
|
||
"> - 1. $F(x)$是一个不减函数。\n",
|
||
"> - 2. $0 < F(x) < 1$，且$$F(-\\infty) = \\lim_{x \\to -\\infty}F(x) = 0, F(\\infty) = \\lim_{x \\to \\infty}F(x) = 1$$。\n",
|
||
"> - 3. $F(x+0) = F(x)$，即$F(x)$是右连续的。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 连续型随机变量：随机变量$\\bf{X}$的取值是连续的（无限多、不可列），这种变量称为**连续型随机变量**。 "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 连续型随机变量的概率密度函数：因为分布函数$F(x)= \\int_{-\\infty}^{x}f(t)dt$，其中，$f(x)$称为随机变量的**概率密度函数**。\n",
|
||
"> 概率密度函数$f(x)$的性质：\n",
|
||
"> - 1. $f(x) \\ ge 0$。\n",
|
||
"> - 2. $\\int_{-\\infty}^{\\infty}f(x)dx = 1$。\n",
|
||
"> - 3. 对于任意实数$x_{1}, x_{2} (x_{1} \\le x_{2})$，有$$P\\{x_{1}< {\\bf{X}} \\le x_{2}\\} = F(x_{2})-F(x_{1}) = \\int_{x_{1}}^{x_{2}}f(x)dx$$\n",
|
||
"> - 4. 若$f(x)$在点$x$处连续，则有$F^{'}(x) =f(x)$。\n",
|
||
"> - 注：对于连续性随机变量，$P\\{a< {\\bf{X}} \\le b\\}=P\\{a\\ge {\\bf{X}} \\le b\\} = P\\{a< {\\bf{X}} < b\\}$。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（分布函数和概率密度的求解）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"已知概率密度函数f(x)=1/(pi*(x**2 + 1))\n",
|
||
"则其分布函数F(x)=atan(x)/pi + 1/2\n",
|
||
"已知分布函数F(x)=(atan(x) + pi/2)/pi\n",
|
||
"则其概率密度函数f(x)=1/(pi*(x**2 + 1))\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# 1. 已知概率密度求解分布函数\n",
|
||
"from sympy import *\n",
|
||
"x = symbols('x')\n",
|
||
"fx = (1/pi) * (1/(1+x**2))\n",
|
||
"print(\"已知概率密度函数f(x)={}\".format(fx))\n",
|
||
"Fx = integrate(fx, (x, -oo, x))\n",
|
||
"print(\"则其分布函数F(x)={}\".format(Fx))\n",
|
||
"# 2. 已知分布函数求解概率密度函数\n",
|
||
"Fx = (1/pi) * (atan(x) + pi/2)\n",
|
||
"fx = diff(Fx, x)\n",
|
||
"print(\"已知分布函数F(x)={}\".format(Fx))\n",
|
||
"print(\"则其概率密度函数f(x)={}\".format(fx))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 三种重要的连续型随机变量：\n",
|
||
"> - 1. 均匀分布：若连续型随机变量${\\bf{X}}$具有概率密度函数$$f(x)=\\left\\{ \\begin{aligned}&\\frac{1}{b-a}, &a < x < b \\\\ &0, &其它 \\end{aligned}\\right.$$ 则称${\\bf{X}}$在区间$(a, b)$上服从**均匀分布**，记为${\\bf{X}} \\sim U(a, b)$。\n",
|
||
"> - 2. 指数分布：若连续型随机变量${\\bf{X}}$具有概率密度函数$$f(x)=\\left \\{ \\begin{aligned} &\\frac{1}{\\theta}e^{-x/\\theta}, &x>0 \\\\ &0, &其它\\end{aligned}\\right.$$其中$\\theta > 0$为常数，则称${\\bf{X}}$服从参数为$\\theta$的**指数分布**。\n",
|
||
"> - 3. 正态分布：若连续型随机变量${\\bf{X}}$具有概率密度函数$$f(x)=\\frac{1}{\\sqrt{2\\pi \\sigma}}e^{-\\frac{(x-\\mu)^2}{2\\sigma ^ {2}}}, -\\infty < x < \\infty$$其中，$\\mu, \\sigma (\\sigma > 0)$为常数，则称为${\\bf{X}}$服从参数为$\\mu, \\sigma$的**正态分布或高斯分布**，记为${\\bf{X}} \\sim N(\\mu, \\sigma ^{2})$。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（三种重要的连续型随机变量）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x432 with 6 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"from sympy import *\n",
|
||
"import matplotlib.pyplot as plt \n",
|
||
"\n",
|
||
"# 1. 均匀分布 U(a, b), \n",
|
||
"a, b = 1, 6\n",
|
||
"x1 = symbols(\"x1\")\n",
|
||
"f1x = (1 / (b - a)) \n",
|
||
"F1x = integrate(f1x, (x1, a, x1))\n",
|
||
"# 2. 指数分布，theta = 1\n",
|
||
"theta = 1\n",
|
||
"x2 = symbols(\"x2\")\n",
|
||
"f2x = (1/ theta) * (exp(-x2/theta)) \n",
|
||
"F2x = integrate(f2x, (x2, 0, x2))\n",
|
||
"# 3. 正态分布 N(mu, sigma^2) ~ (0, 1), (0, 5), (2, 5)\n",
|
||
"x3 = symbols(\"x3\")\n",
|
||
"mu1, sigma1 = 0, 1\n",
|
||
"f3x = (1/sqrt(2*pi*sigma1))*exp(-(x3 - mu1)**2 / (2*(sigma1**2)))\n",
|
||
"F3x = integrate(f3x)\n",
|
||
"\n",
|
||
"# 画图 \n",
|
||
"x1_1 = [f1x for i in np.arange(1, 7, 0.1)] # f1x的纵坐标\n",
|
||
"x1_2 = [F1x.evalf(subs={x1:i}) for i in np.arange(1, 7, step=0.1)] # F1x的纵坐标\n",
|
||
"x2_1 = [f2x.evalf(subs={x2:i}) for i in np.arange(0, 10, 0.1)]\n",
|
||
"x2_2 = [F2x.evalf(subs={x2:i}) for i in np.arange(0, 10, 0.1)]\n",
|
||
"x3_1 = [f3x.evalf(subs={x3:i}) for i in np.arange(-10, 10, 0.1)]\n",
|
||
"x3_2 = [F3x.evalf(subs={x3:i}) for i in np.arange(-10, 10, 0.1)]\n",
|
||
"\n",
|
||
"fig = plt.figure(figsize=(10, 6))\n",
|
||
"plt.subplot(3, 2, 1)\n",
|
||
"plt.plot(list(np.arange(1, 7, 0.1)), x1_1)\n",
|
||
"plt.title(\"Union Distribution Probability\")\n",
|
||
"plt.xlabel('x1')\n",
|
||
"plt.ylabel('f1x')\n",
|
||
"plt.xlim(0, 10)\n",
|
||
"plt.subplot(3,2, 2)\n",
|
||
"plt.plot(list(np.arange(1, 7, 0.1)), x1_2)\n",
|
||
"plt.title(\"Union Distribution\")\n",
|
||
"plt.xlabel('x1')\n",
|
||
"plt.ylabel('F1x')\n",
|
||
"plt.xlim(0, 10)\n",
|
||
"plt.subplot(3, 2, 3)\n",
|
||
"plt.plot(list(np.arange(0, 10, 0.1)), x2_1)\n",
|
||
"plt.title(\"EXP Distribution Probability\")\n",
|
||
"plt.xlabel('x2')\n",
|
||
"plt.ylabel('f2x')\n",
|
||
"plt.subplot(3, 2, 4)\n",
|
||
"plt.plot(list(np.arange(0, 10, 0.1)), x2_2)\n",
|
||
"plt.title(\"EXP Distribution\")\n",
|
||
"plt.xlabel('x2')\n",
|
||
"plt.ylabel('F2x')\n",
|
||
"plt.subplot(3, 2, 5)\n",
|
||
"plt.plot(list(np.arange(-10, 10, 0.1)), x3_1)\n",
|
||
"plt.title(\"Normalization Distribution Probability\")\n",
|
||
"plt.xlabel('x3')\n",
|
||
"plt.ylabel('f3x')\n",
|
||
"plt.subplot(3, 2, 6)\n",
|
||
"plt.plot(list(np.arange(-10, 10, 0.1)), x3_2)\n",
|
||
"plt.title(\"Normalization Distribution\")\n",
|
||
"plt.xlabel('x3')\n",
|
||
"plt.ylabel('F3x')\n",
|
||
"fig.tight_layout(pad=0.4, w_pad=0, h_pad=0)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"[scipy.stats包中包含了统计学一些专用的概率密度函数及分布函数以及其它的功能](https://docs.scipy.org/doc/scipy/tutorial/stats.html#performance-issues-and-cautionary-remarks)，它是一个专门用来进行统计学方法调用的包"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.4 一维随机变量的数字特征：期望、方差、分位数与中位数"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 数学期望（均值） \n",
|
||
"对于离散型随机变量： 设离散型随机变量${\\bf{X}}$的分布律为 $$P{{\\bf{X}}=x_{k}}=p_{k}, k = 1, 2, \\cdots, n.$$ 若级数 $$\\sum_{k=1}^{\\infty}x_{k}p_{k}$$绝对收敛，则称级数$\\sum_{k=1}^{\\infty}x_{k}p_{k}$的和为随机变量${\\bf{X}}$的**数学期望**，记为 $$E({\\bf{X}})=\\sum_{k=1}^{\\infty}x_{k}p_{k}$$\n",
|
||
"对于连续型随机变量：设连续型随机变量${\\bf{X}}$的概率密度为$f(x)$，若积分 $$\\int_{-\\infty}^{\\infty}xf(x)dx$$绝对收敛，则称积分$\\int_{-\\infty}^{\\infty}xf(x)dx$的值为随机变量${\\bf{X}}$的**数学期望**，记为$$E({\\bf{X}}) = \\int_{-\\infty}^{\\infty}xf(x)dx$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 期望的几个重要性质：\n",
|
||
"> - 1.设$C$是常数，有$E(C)=C$。\n",
|
||
"> - 2.设${\\bf{X}}$是一个随机变量，$C$是常数，则有$$E(C{\\bf{X}})=CE({\\bf{X}})$$\n",
|
||
"> - 3.设${\\bf{X}}, {\\bf{Y}}$是两个随机变量，则有$$E({\\bf{X}+\\bf{Y}}) = E({\\bf{X}}) + E({\\bf{Y}})$$\n",
|
||
"> - 4.设${\\bf{X}}, {\\bf{Y}}$是相互独立的随机变量，则有$$E({\\bf{XY}})=E({\\bf{X}})E({\\bf{Y}})$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 常见分布的数学期望：\n",
|
||
"> - 1. 0-1分布：$E({\\bf{X}})=p$\n",
|
||
"> - 2. 二项分布：$E({\\bf{X}}) = np$\n",
|
||
"> - 3. 泊松分布：$E({\\bf{X}}) = \\lambda$\n",
|
||
"> - 4. 均匀分布：$E({\\bf{X}}) = \\frac{a+b}{2}$\n",
|
||
"> - 5. 指数分布：$E({\\bf{X}}) = \\frac{1}{\\theta}$\n",
|
||
"> - 6. 正态分布：$E({\\bf{X}}) = \\mu$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 方差和标准差 \n",
|
||
"设${\\bf{X}}$是一个随机变量，若$E\\{[{\\bf{X}} - E({\\bf{X}})]^{2}\\}$存在，则称$E\\{[{\\bf{X}} - E({\\bf{X}})]^{2}\\}$为${\\bf{X}}$的**方差**，记为$D({\\bf{X}})或Var({\\bf{X}})$，即$$D({\\bf{X}})=Var({\\bf{X}})=E\\{[{\\bf{X}} - E({\\bf{X}})]^{2}\\}$$ 引入$\\sqrt{D({\\bf{X}})}$，记为$\\sigma{(\\bf{X})}$，称为**标准差或均方差**。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 方差化简计算公式：$D({\\bf{X}})=E({\\bf{X}}^{2}) - [E({\\bf{X}})]^{2}$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 方差的性质：\n",
|
||
"> - 1. 设$C$是常数，则$D(C)=0$\n",
|
||
"> - 2. 设$\\bf{X}$是随机变量， $C$是常数，则$$D(C{\\bf{X}})=C^{2}D({\\bf{X}}), D({\\bf{X}}+C)=D({\\bf{X}})$$\n",
|
||
"> - 3. 设$\\bf{X}, \\bf{Y}$是两个随机变量，则有$$D({\\bf{X}}+{\\bf{Y}}) = D({\\bf{X}})+D({\\bf{Y}}) + 2E\\{({\\bf{X}} - E({\\bf{X}}))({\\bf{Y}} - E({\\bf{Y}}))\\}$$ 特别地，若$\\bf{X}, \\bf{Y}$相互独立，则有$$D({\\bf{X}}+{\\bf{Y}}) = D({\\bf{X}})+D({\\bf{Y}})$$\n",
|
||
"> - 4. $D({\\bf{X}})=0$的充分必要条件是${\\bf{X}}$以概率$1$取常数$E({\\bf{X}})$，即$$P\\{{\\bf{X}} = E({\\bf{X}})\\} = 1$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 常见分布的方差：\n",
|
||
"> - 1. 0-1分布：$Var({\\bf{X}}) = p(1-p)$\n",
|
||
"> - 2. 二项分布：$Var({\\bf{X}}) = np(1-p)$\n",
|
||
"> - 3. 泊松分布：$Var({\\bf{X}}) = \\lambda$\n",
|
||
"> - 4. 均匀分布：$Var({\\bf{X}}) = \\frac{(b-a)^{2}}{12}$\n",
|
||
"> - 5. 正态分布：$Var({\\bf{X}}) = \\sigma^2$\n",
|
||
"> - 6. 指数分布：$Var({\\bf{X}}) = \\frac{1}{\\theta^{2}}$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（利用scipy.stats包计算常见分布的均值和方差）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 38,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"0 - 1 分布（p=0.5）的均值：0.5, 方差： 0.25， 标准差：0.5\n",
|
||
"二项分布b(100, 0.5)的均值：50.0, 方差： 25.0， 标准差：5.0\n",
|
||
"泊松分布（lambda=0.6）的均值：0.6, 方差： 0.6， 标准差：0.7745966692414834\n",
|
||
"均匀分布(1, 6)的均值：3.5, 方差： 2.083333333333333， 标准差：1.4433756729740643\n",
|
||
"正态分布(0, 0.1)的均值：0.0, 方差： 0.010000000000000002， 标准差：0.1\n",
|
||
"指数分布(theta = 5)的均值：0.2, 方差： 0.04000000000000001， 标准差：0.2\n",
|
||
"example(x=[1, -1, 2, 3, 4, -1])的均值：[ 1. -1. 2. 3. 4. -1.], 方差： [2.38155178e-29 2.38155178e-29 2.38155178e-29 2.38155178e-29\n",
|
||
" 2.38155178e-29 2.38155178e-29]， 标准差：[4.88011452e-15 4.88011452e-15 4.88011452e-15 4.88011452e-15\n",
|
||
" 4.88011452e-15 4.88011452e-15]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"from scipy.stats import bernoulli # 0 - 1 分布\n",
|
||
"from scipy.stats import binom # 二项分布\n",
|
||
"from scipy.stats import poisson # 泊松分布\n",
|
||
"from scipy.stats import uniform # 均匀分布\n",
|
||
"from scipy.stats import norm # 正态分布\n",
|
||
"from scipy.stats import expon # 指数分布\n",
|
||
"from scipy.stats import rv_continuous # 建立自己的分布函数\n",
|
||
"\n",
|
||
"print(\"0 - 1 分布（p=0.5）的均值：{}, 方差： {}， 标准差：{}\".format(bernoulli(p=0.5).mean(), \n",
|
||
" bernoulli(p=.5).var(), bernoulli(p=0.5).std()))\n",
|
||
"print(\"二项分布b(100, 0.5)的均值：{}, 方差： {}， 标准差：{}\".format(binom(n=100, p=0.5).mean(), \n",
|
||
" binom(n=100, p=0.5).var(), binom(n=100, p=0.5).std()))\n",
|
||
"print(\"泊松分布（lambda=0.6）的均值：{}, 方差： {}， 标准差：{}\".format(poisson(0.6).mean(), poisson(0.6).var(), poisson(0.6).std()))\n",
|
||
"print(\"均匀分布(1, 6)的均值：{}, 方差： {}， 标准差：{}\".format(uniform(1, 5).mean(), uniform(1, 5).var(), uniform(1, 5).std()))\n",
|
||
"print(\"正态分布(0, 0.1)的均值：{}, 方差： {}， 标准差：{}\".format(norm(0, 0.1).mean(), norm(0, 0.1).var(), norm(0, 0.1).std()))\n",
|
||
"print(\"指数分布(theta = 5)的均值：{}, 方差： {}， 标准差：{}\".format(expon(scale=1.0/5.0).mean(), expon(scale=1.0/5.0).var(), expon(scale=1.0/5.0).std()))\n",
|
||
"\n",
|
||
"# 利用rv_continuous创建一个自己的分布函数\n",
|
||
"class My_distribution(rv_continuous):\n",
|
||
" def _cdf(self, x):\n",
|
||
" return np.where(x>0., 1, 0)\n",
|
||
"\n",
|
||
"example = My_distribution(name='example')\n",
|
||
"x= np.array([1, -1, 2, 3, 4, -1])\n",
|
||
"print(\"example(x=[1, -1, 2, 3, 4, -1])的均值：{}, 方差： {}， 标准差：{}\".format(example(x).mean(), example(x).var(), example(x).std()))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 分位数与中位数（连续型随机变量） \n",
|
||
"设连续随机变量 $X$ 的分布函数为 $F(x)$，密度函数为 $p(x)$。 对任意 $p \\in(0,1)$， 称满足条件\n",
|
||
"$$F\\left(x_{p}\\right)=\\int_{-\\infty}^{x_{p}} p(x) \\mathrm{d} x=p$$\n",
|
||
"的 $x_{p}$ 为此分布的 $p$ **分位数**， 又称下侧 $p$ 分位数。\n",
|
||
"\n",
|
||
""
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"分位数与上侧分位数是可以相互转换的， 其转换公式为：$x_{p}^{\\prime}=x_{1-p}, \\quad x_{p}=x_{1-p}^{\\prime}$\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"**中位数就是p=0.5时的分位数点**，设连续随机变量 $X$ 的分布函数为 $F(x)$， 密度函数为 $p(x)$。 称 $p=0.5$ 时的 $p$ 分位数 $x_{0.5}$ 为此分布的中位数，即 $x_{0.5}$ 满足$$F\\left(x_{0.5}\\right)=\\int_{-\\infty}^{x_{0.5}} p(x) \\mathrm{d} x=0.5$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（计算标准正态分布的0.25，0.5（中位数），0.75，0.95分位数点。）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 46,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"标准正态分布（0，1）的0.25分位数点：-0.6744897501960817\n",
|
||
"标准正态分布（0，1）的0.5分位数点：0.0\n",
|
||
"标准正态分布（0，1）的0.75分位数点：0.6744897501960817\n",
|
||
"标准正态分布（0，1）的0.95分位数点：1.6448536269514722\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from scipy.stats import norm\n",
|
||
"\n",
|
||
"print(\"标准正态分布（0，1）的0.25分位数点：{}\".format(norm.ppf(0.25))) \n",
|
||
"print(\"标准正态分布（0，1）的0.5分位数点：{}\".format(norm.ppf(0.5)))\n",
|
||
"print(\"标准正态分布（0，1）的0.75分位数点：{}\".format(norm.ppf(0.75)))\n",
|
||
"print(\"标准正态分布（0，1）的0.95分位数点：{}\".format(norm.ppf(0.95)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# 1.5 多维随机变量及其联合分布、边际分布、条件分布"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 多维随机变量：若随机变量 $X_{1}(\\omega), X_{2}(\\omega), \\cdots, X_{n}(\\omega)$ 定义在同一个基本空间 $\\Omega=\\{\\omega\\}$ 上， 则称\n",
|
||
"$$\\boldsymbol{X}(\\omega)=\\left(X_{1}(\\omega), X_{2}(\\omega), \\cdots, X_{n}(\\omega)\\right)$$\n",
|
||
"是一个多维随机变量，也称为n维随机向量。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 多维随机变量联合分布函数：设 $X=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)$ 是 $n$ 维随机变量， 对任意 $n$ 个实数 $x_{1}, x_{2}, \\cdots, x_{n}$ 所组成的 $n$ 个事件 $X_{1} \\leqslant x_{1},X_{2} \\leqslant x_{2} , \\cdots, X_{n} \\leqslant x_{n} $ 同时发生的概率\n",
|
||
"$$F\\left(x_{1}, x_{2}, \\cdots, x_{n}\\right)=P\\left(X_{1} \\leqslant x_{1}, X_{2} \\leqslant x_{2}, \\cdots, X_{n} \\leqslant x_{n}\\right)$$\n",
|
||
"称为 $n$ 维随机变量 $\\boldsymbol{X}$ 的**联合分布函数**。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 多维随机变量联合概率密度函数：设$n$维随机变量 $X=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)$ 的分布函数为 $F(x_{1}, x_{2}, \\cdots, x_{n})$ 。假如各分量 $x_{1}, x_{2}, \\cdots, x_{n}$ 都是一维连续随机变量，并存在定义在空间上的非负函数 $p(x_{1}, x_{2}, \\cdots, x_{n})$，使得\n",
|
||
"$$F(x, y)=\\int_{-\\infty}^{x_{1}} \\int_{-\\infty}^{x_{2}}\\cdots \\int_{-\\infty}^{x_{n}} p(x_{1}, x_{2}, \\cdots, x_{n}) d x_{1}dx_{2}\\cdots dx_{n}$$\n",
|
||
"则称 $X=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)$ 为$n$维连续随机变量，$p(x_{1}, x_{2}, \\cdots, x_{n})$ 称为 $X=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)$ 的**联合概率密度函数**， 或简称联合密度。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 特例：**二维随机变量** \n",
|
||
"二维随机变量的分布函数：设$(X, Y)$是二维随机变量，对于任意实数$x, y$，二元函数：\n",
|
||
"$$F(x, y)=P\\{X\\le x, Y \\le y\\}$$ \n",
|
||
"称为二维随机变量$(X, Y)$的**分布函数**，或称为随机变量$(X, Y)$的**联合分布函数**。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 分布函数的性质：\n",
|
||
"> - 1. $F(x, y)$是$x, y$的不减函数\n",
|
||
"> - 2. $0 \\le F(x, y) \\le 1$，且$$\\begin{aligned}&对于任意固定的y, F(-\\infty, y) = 0\\\\&对于任意固定的x, F(x, -\\infty)=0\\\\&F(-\\infty, -\\infty)=0, F(\\infty, \\infty)=1\\end{aligned}$$\n",
|
||
"> - 3. $F(x+0, y)=F(x, y), F(x, y+0)=F(x, y)$，即$F(x, y)$关于$x, y$分别右连续\n",
|
||
"> - 4. 对于任意的$(x_{1}, y_{1}), (x_{2}, y_{2}), x_{1} < x_{2}, y_{1} < y_{2}$，有不等式$$F(x_{2},y_{2}) - F(x_{2}, y_{1}) + F(x_{1}, y_{1}) - F(x_{1}, y_{2}) \\ge 0$$恒成立"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  二维随机变量的概率密度函数：对于二维随机变量$(X, Y)$的分布函数$F(x, y)$，如果存在非负可积函数$f(x, y)$，使对于任意$x, y$有\n",
|
||
"$$F(x, y) = \\int_{-\\infty}^{y}\\int_{-\\infty}^{x}f(u, v)dudv$$ \n",
|
||
"则称$(X, Y)$是连续型的二维随机变量，函数$f(x, y)$称为二维随机变量$(X, Y)$的概率密度，或称为随机变量$X和Y$的联合概率密度。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 联合概率密度$f(x, y)$的性质：\n",
|
||
"> - 1. $f(x, y) \\ ge 0$ \n",
|
||
"> - 2. $\\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty}f(x, y)dxdy = 1$\n",
|
||
"> - 3. 若$f(x, y)$在点$(x, y)$连续，则有$$\\frac{\\partial^{2} F(x, y)}{\\partial x\\partial y} = f(x, y)$$\n",
|
||
"> - 4. 设$G$是$xOy$平面上的区域，点$(X, Y)$落在$G$内的概率为：$$P\\{(X, Y) \\in G\\} = \\iint\\limits_{G}f(x, y)dxdy$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（绘制二维概率密度函数图像）[代码参考](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.multivariate_normal.html#scipy.stats.multivariate_normal)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 61,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 864x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"C:\\Users\\13541\\AppData\\Local\\Temp\\ipykernel_11684\\2054532681.py:21: UserWarning: The following kwargs were not used by contour: 'rstride', 'cstride'\n",
|
||
" ax2.contourf(x, y, rv.pdf(pos), rstride=50, cstride=50, cmap='jet')\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": "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",
|
||
"text/plain": [
|
||
"<Figure size 576x432 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"from scipy import stats\n",
|
||
"from mpl_toolkits.mplot3d import axes3d\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"x, y = np.mgrid[-5:5:0.01, -5:5:0.01]\n",
|
||
"pos = np.dstack((x, y))\n",
|
||
"rv = stats.multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])\n",
|
||
"z = rv.pdf(pos)\n",
|
||
"# 曲面图\n",
|
||
"plt.figure('Surface', facecolor='lightgray', figsize=(12, 8))\n",
|
||
"ax = plt.axes(projection='3d')\n",
|
||
"ax.set_xlabel('x', fontsize=14)\n",
|
||
"ax.set_ylabel('y', fontsize=14)\n",
|
||
"ax.set_zlabel('f(x, y)', fontsize = 14)\n",
|
||
"ax.plot_surface(x, y, z, rstride=50, cstride=50, cmap='jet')\n",
|
||
"plt.show()\n",
|
||
"# 等高线图\n",
|
||
"fig2 = plt.figure(figsize=(8,6))\n",
|
||
"ax2 = fig2.add_subplot(111)\n",
|
||
"ax2.contourf(x, y, rv.pdf(pos), rstride=50, cstride=50, cmap='jet')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 边际（边缘）分布： \n",
|
||
"二维随机变量$(X, Y)$作为一个整体，具有分布函数$F(x, y)$，$X和Y$都是随机变量，他们也有自己的分布函数，分别记为$F_{X}(x), F_{Y}(y)$，依次为随机变量$(X, Y)$关于$X$和关于$Y$的**边缘分布函数** $$F_{X}(x)=P\\{X\\le x\\}=P\\{X\\le x, Y < \\infty\\}=F(x, \\infty)$$即$F_{X}(x)=F(x, \\infty)$，同理$$F_{Y}(y)=F(\\infty, y)$$\n",
|
||
"对于连续型随机变量$(X, Y)$，设它的概率密度函数为$f(x, y)$，由于 $$F_{X}(x)=F(x, \\infty)=\\int_{-\\infty}^{x}[\\int_{-\\infty}^{\\infty}f(x, y)dy]dx$$则随机变量$X$的**概率密度函数**为：$f_{X}(x)=\\int_{-\\infty}^{\\infty}f(x, y)dy$ \n",
|
||
"同理，随机变量$Y$的**概率密度函数**为：$f_{Y}(y)=\\int_{-\\infty}^{\\infty}f(x, y)dx$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（已知联合分布求边缘分布）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 64,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"关于随机变量X的边缘密度函数为：Piecewise((x + Max(-x, x), (x > 0) & (x < 1)), (0, True))\n",
|
||
"关于随机变量Y的边缘密度函数为：-Max(0, -y, y) + Max(1, -y, y)\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sympy import *\n",
|
||
"\n",
|
||
"x, y = symbols('x, y')\n",
|
||
"fxy = 1\n",
|
||
"pxy = Piecewise((fxy, And(x > 0, x < 1, y > -x, y < x)), (0, True))\n",
|
||
"fXx = integrate(pxy, (y, -oo, oo))\n",
|
||
"pprint(\"关于随机变量X的边缘密度函数为：{}\".format(fXx))\n",
|
||
"fYy = integrate(pxy, (x, -oo, oo))\n",
|
||
"pprint(\"关于随机变量Y的边缘密度函数为：{}\".format(fYy))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  **边际（边缘）分布列**：在二维离散随机变量 $(X, Y)$ 的联合分布列 $\\left\\{P\\left(X=x_{i}, Y=y_{j}\\right)\\right\\}$ 中， 对 $j$ 求和所得的分布列$$\\sum_{j=1}^{\\infty} P\\left(X=x_{i}, Y=y_{j}\\right)=P\\left(X=x_{i}\\right), \\quad i=1,2, \\cdots$$ \n",
|
||
"  被称为 $X$ 的边际分布列。 类似地， 对 $i$ 求和所得的分布列 $$\\sum_{i=1}^{\\infty} P\\left(X=x_{i}, Y=y_{j}\\right)=P\\left(Y=y_{j}\\right), \\quad j=1,2, \\cdots$$ \n",
|
||
"  被称为 $Y$ 的边际分布列。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 条件分布：由条件概率引出条件概率分布。 \n",
|
||
"设$(X, Y)$是二维离散型随机变量，其分布律为$$P\\{X=x_{i}, Y=y_{j}\\}=p_{ij}, i,j=1,2,\\cdots .$$ $(X, Y)$关于$X$和关于$Y$的边缘分布分别为\n",
|
||
"$$\\begin{aligned}& P\\{X=x_{i}\\}=p_{i}=\\sum_{j=1}^{\\infty}p_{ij}, i=1,2,\\cdots .\\\\&P\\{Y=y_{j}\\}=p_{j}=\\sum_{i=1}^{\\infty}p_{ij}, j=1,2,\\cdots . \\end{aligned}$$\n",
|
||
"设$P_{\\cdot j} > 0$，考虑在事件$\\{Y=y_{j}\\}$已发生的条件下事件$\\{X=x_{i}\\}$发生的概率，由条件概率公式得$$P\\{X=x_{i}|Y=y_{j}\\} = \\frac{P\\{X=x_{i}, Y=y_{j}\\}}{P\\{Y=y_{j}\\}} = \\frac{p_{ij}}{p_{\\cdot j}}, i=1,2,\\cdots .$$上式称为在$Y=y_{j}$条件下随机变量$X$得**条件分布率**，同理$$P\\{Y=y_{j}|X=x_{i}\\} = \\frac{P\\{Y=y_{j}, X=x_{i}\\}}{P\\{X=x_{i}\\}} = \\frac{p_{ij}}{p_{i \\cdot}}, i=1,2,\\cdots .$$称为在$X=x_{i}$条件下随机变量$Y$得**条件分布率**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 条件分布得性质：\n",
|
||
"> - 1. $$P\\{X=x_{i}|Y=y_{j}\\} \\ge 0$$\n",
|
||
"> - 2. $$\\sum_{i=1}^{\\infty}P\\{X=x_{i}|Y=y_{j}\\} = \\sum_{i=1}^{\\infty}\\frac{p_{ij}}{p_{\\cdot j}} =\\frac{1} {p_{\\cdot j}}\\sum_{i=1}^{\\infty}p_{ij} = \\frac{p_{\\cdot j}}{p_{\\cdot j}} = 1$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  连续型随机变量条件分布： \n",
|
||
"设二维随机变量$(X, Y)$得概率密度为$f(x, y)$，$(X, Y)$关于$Y$得边缘概率密度为$f_{Y}(y)$. 若对于固定得$y, f_{Y}(y) > 0$，则称$\\frac{f(x, y)}{f_{Y}(y)}$为在$Y = y$条件下$X$的**条件概率密度函数**，记为\n",
|
||
"$$f_{X|Y}(x|y) = \\frac{f(x, y)}{f_{Y}(y)}$$\n",
|
||
"称$\\int_{-\\infty}^{x}f_{X|Y}(x|y)dx = \\int_{-\\infty}^{x}\\frac{f(x, y)}{f_{Y}(y)}dx$为在$Y = y$条件下$X$的**条件分布函数**，记为$P\\{X\\le x|Y =y\\}或F_{X|Y}(x|y)$，即\n",
|
||
"$$F_{X|Y}(x|y)=P\\{X\\le x|Y =y\\}=\\int_{-\\infty}^{x}\\frac{f(x, y)}{f_{Y}(y)}dx.$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 连续随机变量的贝叶斯公式和全概率公式：\n",
|
||
"> - 1. 全概率公式$$\\begin{aligned}&p_{Y}(y)=\\int_{-\\infty}^{\\infty} p_{X}(x) p(y \\mid x) \\mathrm{d} x, \\\\&p_{\\chi}(x)=\\int_{-\\infty}^{\\infty} p_{Y}(y) p(x \\mid y) \\mathrm{d} y .\\end{aligned}$$\n",
|
||
"> - 2. 贝叶斯公式$$\\begin{aligned}&p(x \\mid y)=\\frac{p_{X}(x) p(y \\mid x)}{\\int_{-\\infty}^{\\infty} p_{X}(x) p(y \\mid x) \\mathrm{d} x},\\\\&p(y \\mid x)=\\frac{p_{Y}(y) p(x \\mid y)}{\\int_{-\\infty}^{\\infty} p_{Y}(y) p(x \\mid y) \\mathrm{d} y} .\\end{aligned}$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码(求解边际分布列)：设在一段时间内进人某一商店的顾客人数 $X$ 服从泊松分布 $P(\\lambda)$， 每个顾客购买某种物品的概率为 $p$, 并且各个顾客是否购买该种物品相互独立， 求进入商店的顾客购买这种物品的人数 $Y$ 的分布列。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 76,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"进入商店人数(k)的概率分布P(X=k) = lamda**k*exp(-lamda)/factorial(k)\n",
|
||
"在进入商店人数（k）确定的条件下，客户买某种商品人数的条件分布P(Y=m|X =k)=p**m*(1 - p)**(k - m)*factorial(k)/(factorial(m)*factorial(k - m))\n",
|
||
"进入商店的顾客购买这种商品人数Y的分布列P(Y=m)=lamda**m*p**m*exp(-lamda)*exp(-lamda*(p - 1))/factorial(m)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/latex": [
|
||
"$\\displaystyle \\frac{\\lambda^{m} p^{m} e^{- \\lambda} e^{- \\lambda \\left(p - 1\\right)}}{m!}$"
|
||
],
|
||
"text/plain": [
|
||
"lamda**m*p**m*exp(-lamda)*exp(-lamda*(p - 1))/factorial(m)"
|
||
]
|
||
},
|
||
"execution_count": 76,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sympy import *\n",
|
||
"from sympy.abc import lamda, k, m, x, y, p # 代替symbols(\"lamda, k, m, x, y\") \n",
|
||
"Pxk = (lamda ** k * exp(- lamda)) / factorial(k)\n",
|
||
"print(\"进入商店人数(k)的概率分布P(X=k) = {}\".format(Pxk))\n",
|
||
"Pyx = (factorial(k) / (factorial(m) * factorial(k-m))) * (p ** m) * ((1 - p) ** (k - m))\n",
|
||
"print(\"在进入商店人数（k）确定的条件下，客户买某种商品人数的条件分布P(Y=m|X =k)={}\".format(Pyx))\n",
|
||
"f = Pxk * Pyx\n",
|
||
"Py = summation(f, (k, m, oo))\n",
|
||
"print(\"进入商店的顾客购买这种商品人数Y的分布列P(Y=m)={}\".format(Py))\n",
|
||
"Py"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.6 多维随机变量的数字特征：期望向量、协方差与协方差矩阵、相关系数与相关系数矩阵"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 期望向量 \n",
|
||
"记 $n$ 维随机向量为 $\\boldsymbol{X}=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)^{T}$, 若其每个分量的数学期望都存在， 则称\n",
|
||
"$$E(\\boldsymbol{X})=\\left(E\\left(X_{1}\\right), E\\left(X_{2}\\right), \\cdots, E\\left(X_{n}\\right)\\right)^{T}$$\n",
|
||
"为 $n$ 维随机向量 $\\boldsymbol{X}$ 的数学期望向量（一般为列向量）， 简称为 $\\boldsymbol{X}$ 的数学期望。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 协方差与协方差矩阵 \n",
|
||
"  协方差：$\\operatorname{Cov}(X, Y)=E[(X-E(X))(Y-E(Y))]$ ，衡量的是两个随机变量之间的相互关联的程度\n",
|
||
"1. 当 $\\operatorname{Cov}(X, Y)>0$ 时， 称 $X$ 与 $Y$ 正相关， 这时两个偏差 $(X-E(X))$ 与 $(Y-E(Y))$ 有**同时增加或同时减少的倾向**。 由于 $E(X)$ 与 $E(Y)$ 都是常数， 故等价于 $X$ 与 $Y$ 有同时增加或同时减少的倾向。\n",
|
||
"2. 当 $\\operatorname{Cov}(X, Y)<0$ 时， 称 $X$ 与 $Y$ 负相关, 这时**有 $X$ 增加而 $Y$ 减少的倾向， 或有 $Y$ 增加而 $X$ 减少的倾向**。\n",
|
||
"3. 当 $\\operatorname{Cov}(X, Y)=0$ 时，称 $X$ 与 $Y$ 不相关。 这时可能由两类情况导致:一类是 $X$ 与 $Y$ 的取值毫无关联， 另一类是 $X$ 与 $Y$ 间存有某种非线性关系。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 协方差$\\operatorname{Cov}(X, Y)$的性质：\n",
|
||
"> - 1. $\\operatorname{Cov}(X, Y)=E(X Y)-E(X) E(Y)$\n",
|
||
"> - 2. 若随机变量 $X$ 与 $Y$ 相互独立， 则 $\\operatorname{Cov}(X, Y)=0$， 反之不成立。\n",
|
||
"> - 3. （最重要）对任意二维随机变量 $(X, Y)$， 有$$\\operatorname{Var}(X \\pm Y)=\\operatorname{Var}(X)+\\operatorname{Var}(Y) \\pm 2 \\operatorname{Cov}(X, Y)$$ 该性质表明: 在 $X$ 与 $Y$ 相关的场合,和的方差不等于方差的和。 $X$ 与 $Y$ 的正相关会增加和的方差,负相关会减少和的方差，而在 $X$ 与 $Y$ 不相关的场合，和的方差等于方差的和，即：**若 $X$ 与 $Y$ 不相关**， 则 $\\operatorname{Var}(X \\pm Y)=\\operatorname{Var}(X)+\\operatorname{Var}(Y)$。\n",
|
||
"> - 4. 协方差 $\\operatorname{Cov}(X, Y)$ 的计算与 $X, Y$ 的次序无关， 即 $$\\operatorname{Cov}(X, Y)=\\operatorname{Cov}(Y, X) $$\n",
|
||
"> - 5. 任意随机变量 $X$ 与常数 $a$ 的协方差为零，即 $$\\operatorname{Cov}(X, a)=0$$\n",
|
||
"> - 6. 对任意常数 $a, b$， 有 $$\\operatorname{Cov}(a X, b Y)=a b \\operatorname{Cov}(X, Y) $$\n",
|
||
"> - 7. 设 $X, Y, Z$ 是任意三个随机变量,则 $$\\operatorname{Cov}(X+Y, Z)=\\operatorname{Cov}(X, Z)+\\operatorname{Cov}(Y, Z)$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"🔥例题：设随机变量$(X, Y)$既有概率密度\n",
|
||
"$$\n",
|
||
"f(x, y)= \\left \\{\n",
|
||
"\\begin{aligned}\n",
|
||
" &\\frac{1}{8}(x+y) , &0 \\le x \\le 2, 0 \\le y \\le 2\\\\\n",
|
||
" &0, &其它\n",
|
||
"\\end{aligned}\n",
|
||
" \\right.\n",
|
||
"$$\n",
|
||
"求$E(X), E(Y), E(XY), Cov(X, Y), D(X+Y)$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"✨解：\n",
|
||
"$$\n",
|
||
"\\begin{aligned}\n",
|
||
"&E(X) = \\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty}xf(x, y)dxdy \\\\\n",
|
||
"&E(Y) = \\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty}yf(x, y)dxdy \\\\\n",
|
||
"&E(XY) = \\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty}xyf(x, y)dxdy \\\\\n",
|
||
"&Cov(X, Y) = E(XY) - E(X)E(Y) \\\\\n",
|
||
"&D(X+Y) = D(X) + D(Y) + 2Cov(X, Y) = E(X^{2}) - [E(X)]^{2} + E(Y^{2}) - [E(Y)]^{2} + 2Cov(X, Y)\n",
|
||
"\\end{aligned}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码(求解例题)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 77,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"E(X) = 1.16666666666667\n",
|
||
"E(Y) = 1.16666666666667\n",
|
||
"E(XY) = 1.33333333333333\n",
|
||
"Cov(X, Y) = -0.0277777777777775\n",
|
||
"D(X + Y) = 0.555555555555557\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sympy import *\n",
|
||
"from sympy.abc import x, y \n",
|
||
"f = (1 / 8) * (x + y)\n",
|
||
"fxy = Piecewise((f, And(x >= 0, x <= 2, y >= 0, y <= 2)), (0, True))\n",
|
||
"Ex = integrate(x * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"print(\"E(X) = {}\".format(Ex))\n",
|
||
"Ey = integrate(y * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"print(\"E(Y) = {}\".format(Ey))\n",
|
||
"Exy = integrate(x * y * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"print(\"E(XY) = {}\".format(Exy))\n",
|
||
"cov_xy = Exy - Ex * Ey \n",
|
||
"print(\"Cov(X, Y) = {}\".format(cov_xy))\n",
|
||
"Ex_2 = integrate(x ** 2 * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"Ey_2 = integrate(y ** 2 * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"Dx_y = Ex_2 - (Ex ** 2) + Ey_2 - (Ey ** 2) + 2 * cov_xy\n",
|
||
"print(\"D(X + Y) = {}\".format(Dx_y))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  协方差矩阵：设$n$ 维随机向量为 $\\boldsymbol{X}=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)^{\\prime}$的期望向量为：\n",
|
||
"$$\n",
|
||
"E(\\boldsymbol{X})=\\left(E\\left(X_{1}\\right), E\\left(X_{2}\\right), \\cdots, E\\left(X_{n}\\right)\\right)^{T}\n",
|
||
"$$\n",
|
||
"则\n",
|
||
"$$\n",
|
||
"\\begin{aligned}\n",
|
||
"& E\\left[(\\boldsymbol{X}-E(\\boldsymbol{X}))(\\boldsymbol{X}-E(\\boldsymbol{X}))^{T}\\right] \\\\\n",
|
||
"=&\\left(\\begin{array}{cccc}\n",
|
||
"\\operatorname{Var}\\left(X_{1}\\right) & \\operatorname{Cov}\\left(X_{1}, X_{2}\\right) & \\cdots & \\operatorname{Cov}\\left(X_{1}, X_{n}\\right) \\\\\n",
|
||
"\\operatorname{Cov}\\left(X_{2}, X_{1}\\right) & \\operatorname{Var}\\left(X_{2}\\right) & \\cdots & \\operatorname{Cov}\\left(X_{2}, X_{n}\\right) \\\\\n",
|
||
"\\vdots & \\vdots & & \\vdots \\\\\n",
|
||
"\\operatorname{Cov}\\left(X_{n}, X_{1}\\right) & \\operatorname{Cov}\\left(X_{n}, X_{2}\\right) & \\cdots & \\operatorname{Var}\\left(X_{n}\\right)\n",
|
||
"\\end{array}\\right)\n",
|
||
"\\end{aligned}\n",
|
||
"$$\n",
|
||
"称为该随机向量的方差-协方差矩阵，简称协方差阵，记为 $\\operatorname{Cov}(\\boldsymbol{X})$。\n",
|
||
"> 🦊注：$n$ 维随机向量的协方差矩阵 $\\operatorname{Cov}(\\boldsymbol{X})=\\left(\\operatorname{Cov}\\left(X_{i}, X_{j}\\right)\\right)_{n \\times n}$ 是一个**对称的非负定矩阵**。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（求上一例题的协方差矩阵）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 78,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/latex": [
|
||
"$\\displaystyle \\left[\\begin{matrix}0.305555555555556 & -0.0277777777777775\\\\-0.0277777777777775 & 0.305555555555556\\end{matrix}\\right]$"
|
||
],
|
||
"text/plain": [
|
||
"Matrix([\n",
|
||
"[ 0.305555555555556, -0.0277777777777775],\n",
|
||
"[-0.0277777777777775, 0.305555555555556]])"
|
||
]
|
||
},
|
||
"execution_count": 78,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sympy import *\n",
|
||
"from sympy.abc import x, y \n",
|
||
"f = (1 / 8) * (x + y)\n",
|
||
"fxy = Piecewise((f, And(x >= 0, x <= 2, y >= 0, y <= 2)), (0, True))\n",
|
||
"Ex = integrate(x * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"Ey = integrate(y * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"Exy = integrate(x * y * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"\n",
|
||
"cov_xy = Exy - Ex * Ey \n",
|
||
"var_x = Ex_2 - (Ex ** 2)\n",
|
||
"var_y = Ey_2 - (Ey ** 2)\n",
|
||
"Matrix([[var_x, cov_xy], [cov_xy, var_y]])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 相关系数与相关系数矩阵 \n",
|
||
"  相关系数：设 $(X, Y)$ 是一个二维随机变量， 且 $\\operatorname{Var}(X)=\\sigma_{X}^{2}>0, \\operatorname{Var}(Y)=\\sigma_{Y}^{2}>0$.则称\n",
|
||
"$$\n",
|
||
"\\operatorname{Corr}(X, Y)=\\frac{\\operatorname{Cov}(X, Y)}{\\sqrt{\\operatorname{Var}(X)} \\sqrt{\\operatorname{Var}(Y)}}=\\frac{\\operatorname{Cov}(X, Y)}{\\sigma_{X} \\sigma_{Y}}\n",
|
||
"$$\n",
|
||
"为 $X$ 与 $Y$ 的 **(线性)** 相关系数，记为$\\rho_{xy}或Corr(X, Y)$。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 相关系数$\\rho_{x, y}$的性质：\n",
|
||
"> - 1. $ -1 \\leqslant \\operatorname{Corr}(X, Y) \\leqslant 1$， 或 $|\\operatorname{Corr}(X, Y)| \\leqslant 1$。\n",
|
||
"> - 2. $\\operatorname{Corr}(X, Y)=\\pm 1$ 的充要条件是 $X$ 与 $Y$ 间几乎处处有线性关系, 即存 在 $a(\\neq 0)$ 与 $b$， 使得$$P(Y=a X+b)=1$$\n",
|
||
"> - 3. 相关系数 $\\operatorname{Corr}(X, Y)$ 刻画了 $X$ 与 $Y$ 之间的线性关系强弱， 因此也常称其为 “线性相关系数”。\n",
|
||
"> - 4. 若 $\\operatorname{Corr}(X, Y)=0$， 则称 $X$ 与 $Y$ 不相关。不相关是指 $X$ 与 $Y$ 之间没有线性关系， 但 $X$ 与 $Y$ 之间可能有其他的函数关系， 譬如平方关系、对数关系等。\n",
|
||
"> - 5. 若 $\\operatorname{Corr}(X, Y)=1$， 则称 $X$ 与 $Y$ 完全正相关； 若 $\\operatorname{Corr}(X, Y)=-1$， 则称 $X$ 与 $Y$ 完全负相关。\n",
|
||
"> - 6. 若 $0<|\\operatorname{Corr}(X, Y)|<1$， 则称 $X$ 与 $Y$ 有 “一定程度” 的线性关系。 $|\\operatorname{Corr}(X, Y)|$ 越接近于 1， 则线性相关程度越高； $|\\operatorname{Corr}(X, Y)|$ 越接近于 0 ， 则线性相关程度越低。 而协方差看不出这一点， 若协方差很小， 而其两个标准差 $\\sigma_{X}$ 和 $\\sigma_{Y}$ 也很小， 则其比值就不一定很小。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  相关系数矩阵：类似于协方差矩阵，相关系数矩阵就是把协方差矩阵中每个元素替换成相关系数，具体来说就是：\n",
|
||
"$$\n",
|
||
"\\begin{aligned}\n",
|
||
"& \\operatorname{Corr}(X, Y)=\\frac{\\operatorname{Cov}(X, Y)}{\\sqrt{\\operatorname{Var}(X)} \\sqrt{\\operatorname{Var}(Y)}}=\\frac{\\operatorname{Cov}(X, Y)}{\\sigma_{X} \\sigma_{Y}} \\\\\n",
|
||
"=&\\left(\\begin{array}{cccc}\n",
|
||
"1 & \\operatorname{Corr}\\left(X_{1}, X_{2}\\right) & \\cdots & \\operatorname{Corr}\\left(X_{1}, X_{n}\\right) \\\\\n",
|
||
"\\operatorname{Corr}\\left(X_{2}, X_{1}\\right) & 1 & \\cdots & \\operatorname{Corr}\\left(X_{2}, X_{n}\\right) \\\\\n",
|
||
"\\vdots & \\vdots & & \\vdots \\\\\n",
|
||
"\\operatorname{Corr}\\left(X_{n}, X_{1}\\right) & \\operatorname{Corr}\\left(X_{n}, X_{2}\\right) & \\cdots & 1\n",
|
||
"\\end{array}\\right)\n",
|
||
"\\end{aligned}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（求上一例题的相关系数矩阵）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 79,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/latex": [
|
||
"$\\displaystyle \\left[\\begin{matrix}1 & -0.297520661157021\\\\-0.297520661157021 & 1\\end{matrix}\\right]$"
|
||
],
|
||
"text/plain": [
|
||
"Matrix([\n",
|
||
"[ 1, -0.297520661157021],\n",
|
||
"[-0.297520661157021, 1]])"
|
||
]
|
||
},
|
||
"execution_count": 79,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sympy import *\n",
|
||
"from sympy.abc import x, y \n",
|
||
"f = (1 / 8) * (x + y)\n",
|
||
"fxy = Piecewise((f, And(x >= 0, x <= 2, y >= 0, y <= 2)), (0, True))\n",
|
||
"Ex = integrate(x * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"Ey = integrate(y * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"Exy = integrate(x * y * fxy, (x, -oo, oo), (y, -oo, oo))\n",
|
||
"\n",
|
||
"cov_xy = Exy - Ex * Ey \n",
|
||
"var_x = Ex_2 - (Ex ** 2)\n",
|
||
"var_y = Ey_2 - (Ey ** 2)\n",
|
||
"Matrix([[1, cov_xy/(var_x * var_y)], [cov_xy/(var_x * var_y), 1]])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.7 随机变量序列的收敛状态：依概率收敛、依分布收敛"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 依概率收敛：设 $\\left\\{X_{n}\\right\\}$ 为一随机变量序列， $X$ 为一随机变量， 如果对任意的 $\\varepsilon>0$， 有\n",
|
||
"$$\n",
|
||
"P\\left(\\left|X_{n}-X\\right| \\geqslant \\varepsilon\\right) \\rightarrow 0(n \\rightarrow \\infty)\n",
|
||
"$$\n",
|
||
"则称序列 $\\left\\{X_{n}\\right\\}$ 依概率收敛于 $X$， 记作 $X_{n} \\stackrel{P}{\\longrightarrow} X$。\n",
|
||
"\n",
|
||
"依概率收玫的含义是： $X_{n}$ 对 $X$ 的绝对偏差不小于任一给定量的可能性将随着 $n$增大而愈来愈小。或者说， 绝对偏差 $\\left|X_{n}-X\\right|$ 小于任一给定量的可能性将随着 $n$ 增大而愈来愈接近于 1 , 即$P\\left(\\left|X_{n}-X\\right| \\geqslant \\varepsilon\\right) \\rightarrow 0(n \\rightarrow \\infty)$等价于\n",
|
||
"$$\n",
|
||
"P\\left(\\left|X_{n}-X\\right|<\\varepsilon\\right) \\rightarrow 1 \\quad(n \\rightarrow \\infty) \n",
|
||
"$$\n",
|
||
"特别当 $X$ 为退化分布时， 即 $P(X=c)=1$（像概率p就是一个案例，频率不断趋近于一个常数p，这个p就是概率）， 则称序列 $\\left\\{X_{n}\\right\\}$ 依概率收敛于 $c$， 即 $X_{n} \\stackrel{P}{\\longrightarrow} c$。\n",
|
||
"> 依概率收敛性质：设$X_{n} \\stackrel{P}{\\longrightarrow}a, Y_{n} \\stackrel{P}{\\longrightarrow}{b}$，又设函数$g(x, y)$在点$(a, b)$连续，则$$g(X_{n}, Y_{n}) \\stackrel{P}{\\longrightarrow} g(a, b)$$\n",
|
||
"\n",
|
||
"* 依分布收敛：设随机变量 $X, X_{1}, X_{2}, \\cdots$ 的分布函数分别为 $F(x), F_{1}(x), F_{2}(x), \\cdots$。 若对 $F(x)$ 的任一**连续点** $x$， 都有\n",
|
||
"$$\n",
|
||
"\\lim _{n \\rightarrow \\infty} F_{n}(x)=F(x)\n",
|
||
"$$\n",
|
||
"则称 $\\left\\{F_{n}(x)\\right\\}$ **弱收敛**于 $F(x)$， 记作\n",
|
||
"$$\n",
|
||
"F_{n}(x) \\stackrel{W}{\\longrightarrow} F(x) \n",
|
||
"$$\n",
|
||
"也称相应的随机变量序列 $\\left\\{X_{n}\\right\\}$ 按分布收敛于 $X$， 记作\n",
|
||
"$$\n",
|
||
"X_{n} \\stackrel{L}{\\longrightarrow} X\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 注：依概率收敛可推出依分布收敛，反之不成立。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.8 大数定律"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"大数定律是叙述随机变量序列的前一些项的算数平均值在某种条件下收敛到这些项的均值的算数平均值。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  **（弱大数）辛钦大数定理**：设$X_{1}, X_{2}, \\cdots$是相互独立，服从同一分布的随机变量序列，且$X_{i}, i = 1, 2, \\cdots$的数学期望存在，作前$n$个变量的算数平均$\\overline{X} = \\frac{1}{n} \\sum_{k =1}^{n} X_{k}$, 则对于任意的$\\varepsilon > 0$，有\n",
|
||
"$$\n",
|
||
"\\lim_{n \\rightarrow \\infty} P\\{\\left| \\frac{1}{n} \\sum_{k =1}^{n} X_{k} - \\frac{1}{n} \\sum_{k =1}^{n} E(X_{k}) \\right| < \\varepsilon\\} = \\lim_{n \\rightarrow \\infty} P\\{\\left| \\overline{X} - \\overline{E(X)}\\right| < \\varepsilon\\}=1\n",
|
||
"$$\n",
|
||
"即 $\\overline{X} \\stackrel{P} \\longrightarrow \\overline{E(X)}$，若随机变量序列具有数学期望$E(X_{k}) = \\mu (k = 1, 2, \\cdots)$，则上式变为\n",
|
||
"$$\n",
|
||
"\\lim_{n \\rightarrow \\infty} P\\{\\left| \\frac{1}{n} \\sum_{k =1}^{n} X_{k} - \\mu \\right| < \\varepsilon\\} = \\lim_{n \\rightarrow \\infty} P\\{\\left| \\overline{X} - \\mu \\right| < \\varepsilon\\} = 1\n",
|
||
"$$\n",
|
||
"即 $\\overline{X} \\stackrel{P} \\longrightarrow \\mu$。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  **伯努利大数定理**：设$f_{A}$是$n$次独立重复实验中事件$A$发生的次数，$p$是事件$A$在每次试验中发生的概率，则对于任意正数$\\varepsilon > 0$，有\n",
|
||
"$$\n",
|
||
"\\lim_{n \\rightarrow \\infty} P\\{\\left| \\frac{f_{A}}{n} - p \\right | < \\varepsilon \\} = 1\n",
|
||
"$$\n",
|
||
"或\n",
|
||
"$$\n",
|
||
"\\lim_{n \\rightarrow \\infty} P\\{\\left| \\frac{f_{A}}{n} - p \\right | \\ge \\varepsilon \\} = 0\n",
|
||
"$$\n",
|
||
"即 $\\frac{f_{A}}{n} \\stackrel{P}{\\longrightarrow} p$。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"> 💡大数定理的条件：独立重复事件、重复次数足够多。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"🔥例：使用蒙特卡洛模拟法求定积分\n",
|
||
"\n",
|
||
"设 $0 \\leqslant f(x) \\leqslant 1$, 求 $f(x)$ 在 区间 $[0,1]$ 上的积分值\n",
|
||
"$$\n",
|
||
"J=\\int_{0}^{1} f(x) \\mathrm{d} x\n",
|
||
"$$\n",
|
||
"🦊解:在正方形$\\{0 \\leqslant x \\leqslant 1,0 \\leqslant y \\leqslant 1\\}$内均匀地投点$(x_i,y_i)$，投n个点，点越多越好。如果某个点$y_i \\le f(x_i)$,则认为事件发生，我们计算满足$y_i \\le f(x_i)$点的个数$S_n$，使用大数定律：频率稳定于概率，即：$\\frac{S_n}{n}$就是积分值。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（求解例题）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 100,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 864x432 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"函数y = x^3 的积分值为：0.25\n",
|
||
"蒙特卡洛方法(模拟10次)计算的结果为：0.2\n",
|
||
"蒙特卡洛方法(模拟100次)计算的结果为：0.25\n",
|
||
"蒙特卡洛方法(模拟1000次)计算的结果为：0.247\n",
|
||
"蒙特卡洛方法(模拟10000次)计算的结果为：0.2521\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from scipy import integrate\n",
|
||
"from scipy.stats import uniform\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt \n",
|
||
"from random import choice\n",
|
||
"\n",
|
||
"# 蒙特卡洛原理：将待积分函数看作是某个概率密度分布函数，根据分布函数的定义，那么对函数的积分就转化为求概率的过程。\n",
|
||
"x_arr = np.linspace(0, 1, 1000)\n",
|
||
"y_arr = x_arr ** 3\n",
|
||
"\n",
|
||
"x_n = uniform.rvs(size=100) \n",
|
||
"y_n = uniform.rvs(size=100)\n",
|
||
"plt.figure(figsize=(12, 6))\n",
|
||
"plt.stackplot(x_arr, y_arr, alpha=0.5, color='skyblue')\n",
|
||
"plt.scatter(x_n, y_n)\n",
|
||
"plt.text(1.0, 1.0, r'$y = x^3$')\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"class Montecarlo():\n",
|
||
" def __init__(self, n):\n",
|
||
" self.n = n # 模拟的次数\n",
|
||
" self.fn = 0 \n",
|
||
" def solve(self, x, y, f):\n",
|
||
" for i in range(self.n):\n",
|
||
" a = choice(x)\n",
|
||
" b = choice(y)\n",
|
||
" if f(a) >= b:\n",
|
||
" self.fn += 1\n",
|
||
" else:\n",
|
||
" continue\n",
|
||
" res = self.fn / self.n\n",
|
||
" print(\"蒙特卡洛方法(模拟{}次)计算的结果为：{}\".format(self.n, res))\n",
|
||
"\n",
|
||
"# 求解y = x^3 在区间[0, 1]上的积分值\n",
|
||
"x_1 = np.linspace(0, 1, 1000)\n",
|
||
"y_1 = np.linspace(0, 1, 1000)\n",
|
||
"def f(x):\n",
|
||
" return x ** 3\n",
|
||
"int_f = integrate.quad(f, 0, 1)\n",
|
||
"print(\"函数y = x^3 的积分值为：{}\".format(int_f[0]))\n",
|
||
"monte_10 = Montecarlo(10)\n",
|
||
"monte_10.solve(x_1, y_1, f)\n",
|
||
"monte_100 = Montecarlo(100)\n",
|
||
"monte_100.solve(x_1, y_1, f)\n",
|
||
"monte_1000 = Montecarlo(1000)\n",
|
||
"monte_1000.solve(x_1, y_1, f)\n",
|
||
"monte_10000 = Montecarlo(10000)\n",
|
||
"monte_10000.solve(x_1, y_1, f)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.9 中心极限定理"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"中心极限定理确定在什么条件下，大量随机变量之和的分布逼近于正态分布。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"  **独立同分布的中心极限定理**：设随机变量$X_{1}, X_{2}, \\cdots, X_{n}, \\cdots$相互独立，服从同一分布，且具有数学期望和方差：$E(X_{k}) = \\mu, D(X_{k}) = \\sigma ^{2} (k = 1, 2, \\cdots)$，则随机变量之和$\\sum_{k=1}^{n}X_{k}$的标准化变量\n",
|
||
"$$\n",
|
||
"Y_{n} = \\frac{\\sum_{k=1}^{n}X_{k} - E(\\sum_{k=1}^{n}X_{k})}{\\sqrt{D(\\sum_{k=1}^{n}X_{k})}} = \\frac{\\sum_{k=1}^{n}X_{k} - n\\mu}{\\sqrt{n}\\sigma}\n",
|
||
"$$\n",
|
||
"的分布函数$F_{n}(x)$对于任意$x$满足\n",
|
||
"$$\n",
|
||
"\\begin{aligned}\n",
|
||
"\\lim_{n \\rightarrow \\infty}F_{n}(X)\n",
|
||
" &= \\lim_{n \\rightarrow \\infty}P\\left \\{ \\frac{\\sum_{k=1}^{n}X_{k} - n\\mu}{\\sqrt{n}\\sigma} \\le x \\right \\} \\\\\n",
|
||
" &= \\int_{-\\infty}^{x} \\frac{1}{\\sqrt{2 \\pi}} e^{- t^{2}/ 2}dt \\\\\n",
|
||
" &= \\Phi (x)\n",
|
||
"\\end{aligned}\n",
|
||
"$$\n",
|
||
"即 $Y_{n} \\sim N(n\\mu, \\sigma^{2})$或$\\overline{X} \\sim N(\\mu, \\sigma^{2}/n)$或$\\frac{\\overline{X} - \\mu}{\\sigma / \\sqrt{n}} \\sim N(0, 1)$。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（验证独立同分布的中心极限定理）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 137,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"from sympy import * \n",
|
||
"from scipy.stats import norm # 正态分布\n",
|
||
"from scipy.stats import expon # 指数分布\n",
|
||
"from scipy.stats import uniform # 均匀分布\n",
|
||
"from scipy.stats import poisson # 泊松分布\n",
|
||
"import scipy.stats as ss # 0-1 分布(前文有重名的变量名，不便直接引入) from scipy.stats import bernoulli\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"import random"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 107,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# 1. n个服从正态分布随机变量的和 的分布\n",
|
||
"\n",
|
||
"def norm_sum(mu, sigma, n, x_size):\n",
|
||
" X = 0\n",
|
||
" for i in range(n):\n",
|
||
" x_i = norm(loc=mu[i], scale=sigma[i]).rvs(size=x_size)\n",
|
||
" X += x_i\n",
|
||
" plt.figure(figsize=(10, 8)) \n",
|
||
" plt.hist(X, density=True, histtype='stepfilled', alpha=0.2)\n",
|
||
" plt.title(\"Random variable number n={}\".format(str(n)))\n",
|
||
" plt.xlabel(\"x\")\n",
|
||
" plt.ylabel(\"p(x)\")\n",
|
||
" plt.show()\n",
|
||
"\n",
|
||
"x_size = 10000\n",
|
||
"mu = np.zeros(x_size)\n",
|
||
"sigma = np.random.randint(0, 10, x_size)\n",
|
||
"norm_sum(mu, sigma, 10, x_size)\n",
|
||
"norm_sum(mu, sigma, 100, x_size)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 126,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# 2. n个服从均匀分布随机变量的和 的分布\n",
|
||
"\n",
|
||
"def variable_sum(n, x_size, distribution):\n",
|
||
" X = 0\n",
|
||
" for i in range(n):\n",
|
||
" x_i = distribution.rvs(x_size)\n",
|
||
" X += x_i\n",
|
||
" plt.figure(figsize=(10, 8)) \n",
|
||
" plt.hist(X, density=True, histtype='stepfilled', alpha=0.2)\n",
|
||
" plt.title(\"Random variable number n={}\".format(str(n)))\n",
|
||
" plt.xlabel(\"x\")\n",
|
||
" plt.ylabel(\"p(x)\")\n",
|
||
" plt.show()\n",
|
||
"\n",
|
||
"x_size = 10000\n",
|
||
"loc = np.zeros(x_size)\n",
|
||
"scale = 5\n",
|
||
"distribution = uniform(loc=loc, scale=scale)\n",
|
||
"variable_sum(n=10, x_size=x_size, distribution=distribution)\n",
|
||
"variable_sum(n=100, x_size=x_size, distribution=distribution)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 112,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# 3. n个服从指数分布随机变量的和 的分布\n",
|
||
"\n",
|
||
"x_size = 10000\n",
|
||
"lam = 5\n",
|
||
"distribution = expon(scale=1/lam)\n",
|
||
"variable_sum(n=10, x_size=x_size, distribution=distribution)\n",
|
||
"variable_sum(n=100, x_size=x_size, distribution=distribution)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 116,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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kSWqAoU2SJKkBhjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGmBokyRJaoChTZIkqQGGNkmSpAYY2iRJkhpgaJMkSWqAoU2SJKkBhjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGmBokyRJaoChTZIkqQGGNkmSpAYsHncBknbuqi3bxl2CJGnMnGmTJElqgKFNkiSpASMNbUnWJNmcZCrJyTNs3zfJ+f32y5Ks6NsPTPLZJHcmeedA/0cl+WSSryTZlORPR1m/JEnSfDGy0JZkEXAGcBSwGjg2yeqhbicAt1fVocDpwGl9+73A64Hfn+HQb62qHwGeDfxkkqNGUb8kSdJ8MsqZtiOAqaq6tqruB9YDa4f6rAXO7Zc3AEcmSVXdVVWX0IW3B1TV3VX12X75fuBKYPkIz0GSJGleGGVoOxi4cWB9S982Y5+q2g5sAw7clYMneSzwMuDvHm6hkiRJ812TDyIkWQx8EHhHVV07S58Tk0wmmdy6deueLVCSJGmOjTK03QQcMrC+vG+bsU8fxJYCt+7Csc8CvlZVb5+tQ1WdVVUTVTWxbNmy3albkiRp3hllaLscWJVkZZIlwDpg41CfjcDx/fIxwMVVVTs6aJI304W7181tuZIkSfPXyL4Roaq2JzkJuAhYBJxTVZuSnApMVtVG4GzgvCRTwG10wQ6AJNcDBwBLkhwNvBi4A/hj4CvAlUkA3llV7x7VeUiSJM0HI/0aq6q6ELhwqO0NA8v3Aq+cZd8Vsxw2c1WfJElSK5p8EEGSJGmhMbRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNWCkoS3JmiSbk0wlOXmG7fsmOb/fflmSFX37gUk+m+TOJO8c2udHk1zV7/OOJBnlOUiSJM0HIwttSRYBZwBHAauBY5OsHup2AnB7VR0KnA6c1rffC7we+P0ZDn0m8P8Aq/o/a+a+ekmSpPlllDNtRwBTVXVtVd0PrAfWDvVZC5zbL28AjkySqrqrqi6hC28PSPIk4ICqurSqCngvcPQIz0GSJGleGGVoOxi4cWB9S982Y5+q2g5sAw7cyTG37OSYkiRJe5299kGEJCcmmUwyuXXr1nGXI0mS9LCMMrTdBBwysL68b5uxT5LFwFLg1p0cc/lOjglAVZ1VVRNVNbFs2bLdLF2SJGl+GWVouxxYlWRlkiXAOmDjUJ+NwPH98jHAxf171WZUVTcDdyR5Xv/U6KuBj8996ZIkSfPL4lEduKq2JzkJuAhYBJxTVZuSnApMVtVG4GzgvCRTwG10wQ6AJNcDBwBLkhwNvLiqrgZ+G3gP8EjgU/0fSZKkvdrIQhtAVV0IXDjU9oaB5XuBV86y74pZ2ieBZ8xdlZIkSfPfXvsggiRJ0t7E0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDVgt0JbkkcnWTSqYiRJkjSzHYa2JPskOS7JJ5PcAnwFuDnJ1Un+LMmhe6ZMSZKkhW1nM22fBZ4GnAI8saoOqap/AzwfuBQ4LcmrRlyjJEnSgrd4J9tfVFXfHW6sqtuADwMfTvKIkVQmSZKkB+xwpm06sCV50fC2JMcP9pEkSdLo7OqDCG9Icmb/IMITknwCeNkoC5MkSdIP7Gpo+yng68CXgEuAD1TVMaMqSpIkSQ+2q6HtccARdMHtPuCpSTKyqiRJkvQguxraLgU+XVVrgOcCTwb+cWRVSZIk6UF29vTotBdV1f8BqKp7gN9J8sLRlSVJkqRBO/tw3RUA04FtUFV9Lp3lI6pNkiRJvZ3NtP1Zkn2AjwNXAFuB/YBDgZ8BjgT+BNgyyiIlSZIWuh2Gtqp6ZZLVwK8AvwE8EbgHuAa4EHhLVd078iolSZIWuJ0+iFBVVwNvBj5BF9auAy4HNhjYJEmS9oxdfRDhXOAO4B39+nHAe4FfGkVRkiRJerBdDW3PqKrVA+ufTXL1KAqSJEnSD9vVz2m7MsnzpleS/BgwOZqSJEmSNGxXQ9uPAv+U5Pok1wOfB56b5Kok/zLbTknWJNmcZCrJyTNs3zfJ+f32y6Y/YqTfdkrfvjnJSwba/3OSTUm+nOSDSfbb1ZOVJElq1a7eHl2zuwdOsgg4A/g5uo8EuTzJxv7BhmknALdX1aFJ1gGnAb/cP7G6DjiM7tsX/jbJ0+meXv0dYHVV3ZPkgr7fe3a3PkmSpJbsUmirqhsewrGPAKaq6lqAJOuBtcBgaFsLvLFf3gC8s/9O07XA+qq6D7guyVR/vP/T1/zIJN8FHgX860OoTZIkqSm7env0oTgYuHFgfUvfNmOfqtoObAMOnG3fqroJeCtdeLsZ2FZVfzOS6iVJkuaRUYa2OZfkcXSzcCvpbps+OsmrZul7YpLJJJNbt27dk2VKkiTNuV19T9tDcRNwyMD68r5tpj5bkiwGlgK37mDfFwHXVdVWgCQfAX4CeN/wi1fVWcBZABMTEzUH5yNJe6Wrtmwbdwlz5vDlS8ddgjQyo5xpuxxYlWRlkiV0DwxsHOqzETi+Xz4GuLiqqm9f1z9duhJYBXyB7rbo85I8qn/v25F039IgSZK0VxvZTFtVbU9yEnARsAg4p6o2JTkVmKyqjcDZwHn9gwa30QU7+n4X0D20sB14bVV9D7gsyQbgyr79i/SzaZIkSXuzdBNbe7eJiYmanPSzgNWuven2lTRK3h7V3iDJFVU1Mdze1IMIkiRJC5WhTZIkqQGGNkmSpAYY2iRJkhpgaJMkSWqAoU2SJKkBhjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGmBokyRJaoChTZIkqQGGNkmSpAYY2iRJkhpgaJMkSWqAoU2SJKkBhjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGmBokyRJaoChTZIkqQGGNkmSpAYY2iRJkhpgaJMkSWqAoU2SJKkBhjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGmBokyRJaoChTZIkqQGGNkmSpAYY2iRJkhpgaJMkSWqAoU2SJKkBIw1tSdYk2ZxkKsnJM2zfN8n5/fbLkqwY2HZK3745yUsG2h+bZEOSryS5JsmPj/IcJEmS5oORhbYki4AzgKOA1cCxSVYPdTsBuL2qDgVOB07r910NrAMOA9YA7+qPB/C/gE9X1Y8AzwSuGdU5SJIkzRejnGk7Apiqqmur6n5gPbB2qM9a4Nx+eQNwZJL07eur6r6qug6YAo5IshR4IXA2QFXdX1XfHuE5SJIkzQujDG0HAzcOrG/p22bsU1XbgW3AgTvYdyWwFfirJF9M8u4kjx5N+ZIkSfNHaw8iLAaeA5xZVc8G7gJ+6L1yAElOTDKZZHLr1q17skZJkqQ5N8rQdhNwyMD68r5txj5JFgNLgVt3sO8WYEtVXda3b6ALcT+kqs6qqomqmli2bNnDPBVJkqTxGmVouxxYlWRlkiV0DxZsHOqzETi+Xz4GuLiqqm9f1z9duhJYBXyhqr4B3Jjk3/X7HAlcPcJzkCRJmhcWj+rAVbU9yUnARcAi4Jyq2pTkVGCyqjbSPVBwXpIp4Da6YEff7wK6QLYdeG1Vfa8/9H8C3t8HwWuBXx/VOUiSJM0X6Sa29m4TExM1OTk57jKkh+yqLdvGXYLUhMOXLx13CdLDluSKqpoYbm/tQQRJkqQFydAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDVg87gKkUbpqy7ZxlyBJ0pxwpk2SJKkBIw1tSdYk2ZxkKsnJM2zfN8n5/fbLkqwY2HZK3745yUuG9luU5ItJ/nqU9UuSJM0XIwttSRYBZwBHAauBY5OsHup2AnB7VR0KnA6c1u+7GlgHHAasAd7VH2/a7wLXjKp2SZKk+WaUM21HAFNVdW1V3Q+sB9YO9VkLnNsvbwCOTJK+fX1V3VdV1wFT/fFIshz4BeDdI6xdkiRpXhllaDsYuHFgfUvfNmOfqtoObAMO3Mm+bwf+APj+nFcsSZI0TzX1IEKSlwK3VNUVu9D3xCSTSSa3bt26B6qTJEkanVGGtpuAQwbWl/dtM/ZJshhYCty6g31/Enh5kuvpbrf+bJL3zfTiVXVWVU1U1cSyZcse/tlIkiSN0ShD2+XAqiQrkyyhe7Bg41CfjcDx/fIxwMVVVX37uv7p0pXAKuALVXVKVS2vqhX98S6uqleN8BwkSZLmhZF9uG5VbU9yEnARsAg4p6o2JTkVmKyqjcDZwHlJpoDb6IIYfb8LgKuB7cBrq+p7o6pVkiRpvks3sbV3m5iYqMnJyXGXoTHwGxGkheXw5UvHXYL0sCW5oqomhtubehBBkiRpoTK0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUgMXjLkCSpLly1ZZt4y5hzhy+fOm4S9A840ybJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0YaWhLsibJ5iRTSU6eYfu+Sc7vt1+WZMXAtlP69s1JXtK3HZLks0muTrIpye+Osn5JkqT5YmShLcki4AzgKGA1cGyS1UPdTgBur6pDgdOB0/p9VwPrgMOANcC7+uNtB/5LVa0Gnge8doZjSpIk7XVGOdN2BDBVVddW1f3AemDtUJ+1wLn98gbgyCTp29dX1X1VdR0wBRxRVTdX1ZUAVfUd4Brg4BGegyRJ0rwwytB2MHDjwPoWfjhgPdCnqrYD24ADd2Xf/lbqs4HL5rJoSZKk+ajJBxGS7A98GHhdVd0xS58Tk0wmmdy6deueLVCSJGmOjTK03QQcMrC+vG+bsU+SxcBS4NYd7ZvkEXSB7f1V9ZHZXryqzqqqiaqaWLZs2cM8FUmSpPEaZWi7HFiVZGWSJXQPFmwc6rMROL5fPga4uKqqb1/XP126ElgFfKF/v9vZwDVV9T9HWLskSdK8snhUB66q7UlOAi4CFgHnVNWmJKcCk1W1kS6AnZdkCriNLtjR97sAuJruidHXVtX3kjwf+FXgqiRf6l/qj6rqwlGdhyRJ0nyQbmJr7zYxMVGTk5PjLkNjcNWWbeMuQZIeksOXLx13CRqTJFdU1cRwe5MPIkiSJC00hjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGmBokyRJaoChTZIkqQGGNkmSpAYY2iRJkhpgaJMkSWqAoU2SJKkBhjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYvHXYDmn6u2bBt3CZIkaYgzbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2SJEkNMLRJkiQ1wNAmSZLUAEObJElSAwxtkiRJDTC0SZIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDFo+7AEmS9MOu2rJt3CXMmcOXLx13CXsFZ9okSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGmBokyRJaoAf+TFH9qZHsyVJ0vwz0pm2JGuSbE4yleTkGbbvm+T8fvtlSVYMbDulb9+c5CW7ekxJkqS90chCW5JFwBnAUcBq4Ngkq4e6nQDcXlWHAqcDp/X7rgbWAYcBa4B3JVm0i8eUJEna64xypu0IYKqqrq2q+4H1wNqhPmuBc/vlDcCRSdK3r6+q+6rqOmCqP96uHFOSJGmvM8r3tB0M3DiwvgX4sdn6VNX2JNuAA/v2S4f2Pbhf3tkxJUnSPLK3vO973F/Htdc+iJDkRODEfvXOJJvHWc8MDgK+Ne4iGuOY7R7Ha/c4XrvPMds9jtfuW6hj9tSZGkcZ2m4CDhlYX963zdRnS5LFwFLg1p3su7NjAlBVZwFnPdTiRy3JZFVNjLuOljhmu8fx2j2O1+5zzHaP47X7HLMHG+V72i4HViVZmWQJ3YMFG4f6bASO75ePAS6uqurb1/VPl64EVgFf2MVjSpIk7XVGNtPWv0ftJOAiYBFwTlVtSnIqMFlVG4GzgfOSTAG30YUw+n4XAFcD24HXVtX3AGY65qjOQZIkab5IN7GlPS3Jif0tXO0ix2z3OF67x/HafY7Z7nG8dp9j9mCGNkmSpAb43aOSJEkNMLSNUP8tDl9M8tf9+vv7r+D6cpJzkjyib//pJNuSfKn/84bxVj4+M4zZe5JcNzA2z+rbk+Qd/deZ/UuS54y18DGZYbz+YWCs/jXJx/p2rzEgyfVJrurHYLJve3ySzyT5Wv/fx/XtC/4am2W8/izJV/ox+WiSx/btK5LcM3CN/cVYix+TWcbsjUluGhibnx/oP+NXNi4Us4zX+QNjdX2SL/XtC/4a22s/p22e+F3gGuCAfv39wKv65Q8Avwmc2a//Q1W9dM+WNy8NjxnAf62qDUP9jqJ7qngV3Qcsn8nC/KDlB41XVb1gekOSDwMfH+jrNdb5maoa/Nynk4G/q6o/Tfd9xicDf4jX2LTh8foMcEr/sNlpwCl04wXw9ap61p4ucB4aHjOA06vqrYMNefBXNj4Z+NskT59+8G4BedB4VdUvTy8neRsw+Mm8C/oac6ZtRJIsB34BePd0W1VdWD26jzBZPq765qOZxmwH1gLv7YfzUuCxSZ400gLnmR2NV5IDgJ8FPraHy2rR4NfpnQscPdC+oK+xmVTV31TV9n71Uvx37OGY7SsbRTfbDfwS8MFx1zJfGNpG5+3AHwDfH97Q3xb9VeDTA80/nuSfk3wqyWF7psR55+3MPGZv6W/FnJ5k375tpq9JO5iF5e3Mco3RBY+/q6o7Btq8xqCAv0lyRbpvTQF4QlXd3C9/A3hCv+w1NvN4DfoN4FMD6yv72/V/n+QFM/RfCGYbs5P6f8fOmb4Fj9cY7PgaewHwzar62kDbgr7GDG0jkOSlwC1VdcUsXd4FfK6q/qFfvxJ4alU9E/hzFuDsyA7G7BTgR4DnAo/nB7dhFrRduMaO5cH/d7rgr7He86vqOXS3Pl+b5IWDG/tZcB+p/4FZxyvJH9N9jub7+6abgadU1bOB3wM+0M/4LjQzjdmZwNOAZ9GN09vGV968s6O/k8P/ji34a8zQNho/Cbw8yfXAeuBnk7wPIMmfAMvoLjgAquqOqrqzX74QeESSg/Z41eM145hV1c397an7gL/iB7cOduVr0vZmO7rGDqIbp09Od/Ya61TVTf1/bwE+SjdO35y+7dn/95a++0K/xmYbL5L8GvBS4Ff6oEt/i+/WfvkK4OvA08dQ9ljNNGZV9c2q+l5VfR/4S/x37AE7uMYWA68Azh/ou+CvMUPbCFTVKVW1vKpW0L3J9OKqelWS3wReAhzb/+UFIMkT+3v3JDmC7udy6xhKH5sdjNn0L9PQ3fL7cr/LRuDV/RN+zwO2Ddzi2uvNNl795mOAv66qe6f7e41Bkkcnecz0MvBiuutp8Ov0jucHD28s6GtstvFKsobutvzLq+rugf7Lkizql/8t3QMc1+75ysdnB2M2+F7I/8iD/x2b6SsbF4Qd/J0EeBHwlaraMtB/wV9jPj26Z/0FcAPw+f7350eq6lS6X7K/lWQ7cA+wbvr/XsX7kywDAnwJeE3ffiHw83Rv3L0b+PWxVDc/rQP+dKjNa6x7r9pH+797i4EPVNWnk1wOXJDkBLq/n7/U91/o19hs4zUF7At8pt92aVW9BnghcGqS79K9z/I1VXXbeEofm9nG7Lx0H1dUwPXA/ws7/srGBWLG8eq3reOHH0BY8NeY34ggSZLUAG+PSpIkNcDQJkmS1ABDmyRJUgMMbZIkSQ0wtEmSJDXA0CZJktQAQ5skSVIDDG2StBuSPLf/4u/9+k9035TkGeOuS9Lezw/XlaTdlOTNwH7AI4EtVfU/xlySpAXA0CZJuynJEuBy4F7gJxbYVw9JGhNvj0rS7jsQ2B94DN2MmySNnDNtkrSbkmwE1gMrgSdV1UljLknSArB43AVIUkuSvBr4blV9IMki4J+S/GxVXTzu2iTt3ZxpkyRJaoDvaZMkSWqAoU2SJKkBhjZJkqQGGNokSZIaYGiTJElqgKFNkiSpAYY2SZKkBhjaJEmSGvB/AalVnxGQWcnqAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# 4. n个服从泊松分布随机变量的和 的分布\n",
|
||
"\n",
|
||
"x_size = 10000\n",
|
||
"mu = 5\n",
|
||
"distribution = poisson(mu=mu)\n",
|
||
"variable_sum(n=10, x_size=x_size, distribution=distribution)\n",
|
||
"variable_sum(n=100, x_size=x_size, distribution=distribution)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 140,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 720x576 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# 5. n个服从（0- 1）分布随机变量的和 的分布\n",
|
||
"\n",
|
||
"def bernoulli_sum(n, x_size, p):\n",
|
||
" X = 0\n",
|
||
" for i in range(n):\n",
|
||
" x_i = ss.bernoulli.rvs(p, size=x_size)\n",
|
||
" X += x_i\n",
|
||
" plt.figure(figsize=(10, 8)) \n",
|
||
" plt.hist(X, density=True, histtype='stepfilled', alpha=0.2)\n",
|
||
" plt.title(\"Random variable number n={}\".format(str(n)))\n",
|
||
" plt.xlabel(\"x\")\n",
|
||
" plt.ylabel(\"p(x)\")\n",
|
||
" plt.show()\n",
|
||
"\n",
|
||
"x_size = 10000\n",
|
||
"p = 0.4\n",
|
||
"bernoulli_sum(n=10, x_size=x_size, p=p)\n",
|
||
"bernoulli_sum(n=100, x_size=x_size, p=p)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 1.10 数学建模案例分析：投资组合分析"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 📕任务：GitModel公司是一家专业的投资银行，志在帮助客户更好地管理资产。客户手头上有一笔100万的资金，希望将这笔钱投入股票市场进行投资理财，投资人看中了两个股票$A$、$B$，股票分析师通过对股票$A$、$B$的历史数据分析发现：股票$A$的平均收益率近似服从$N(0.1,0.01)$，股票B的平均收益率近似服从$N(0.3,0.04)$。现在客户希望通过分析得出投资股票$A$、$B$的最佳组合（在预期收益率确定情况下最小风险时，需要投资$A$、$B$的份额）。"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* 🦊解：由题意知：\n",
|
||
"股票$A, B$的收益$X, Y$服从如下分布\n",
|
||
"$$\n",
|
||
" X \\sim N(0.1, 0.01), Y \\sim N(0.3, 0.04)\n",
|
||
"$$\n",
|
||
"设投资股票$A$的份额为$p$, 则投资股票$B$的份额为$(1-p)$，其中$(0 \\le p \\le 1)$，总收益为$Z$，则\n",
|
||
"$$\n",
|
||
"Z = pX + (1-p)Y\n",
|
||
"$$\n",
|
||
"均值体现股票的平均收益率高低，方差体现股票的风险大小。则平均收益率为\n",
|
||
"$$\n",
|
||
"E(Z) = E(pX + (1-p)Y) = pE(X) + (1-p)E(Y)\n",
|
||
"$$\n",
|
||
"风险大小(目标函数)为\n",
|
||
"$$\n",
|
||
"\\begin{aligned}\n",
|
||
"D(Z) &= D(pX + (1-p)Y) \\\\\n",
|
||
"&=D(pX) + D((1-p)Y) + 2Cov(pX, (1-p)Y) \\\\\n",
|
||
"&= p^{2}D(X) + (1-p)^{2}D(Y) + 2p(1-p)Cov(X, Y)\n",
|
||
"\\end{aligned}\n",
|
||
"$$\n",
|
||
"由题意知，需要找到一个合适的$p*$，使得风险$D(Z)$最小\n",
|
||
"$$\n",
|
||
"venture = \\underset{p^{*}}{argmin}\\left[D(Z) \\right ] = \\underset{p^{*}}{argmin}\\left [p^{2}D(X) + (1-p)^{2}D(Y) + 2p(1-p)Cov(X, Y) \\right ]\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"python代码（求解上题）"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 188,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"当相关系数rho=-1.00时：\n",
|
||
"\t风险系数波动（方差）为：0.0000\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.666666666666667, 投资股票B的份额应为：10w *0.333333333333333\n",
|
||
"当相关系数rho=-0.90时：\n",
|
||
"\t风险系数波动（方差）为：0.0009\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.674418604651163, 投资股票B的份额应为：10w *0.325581395348837\n",
|
||
"当相关系数rho=-0.80时：\n",
|
||
"\t风险系数波动（方差）为：0.0018\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.682926829268293, 投资股票B的份额应为：10w *0.317073170731707\n",
|
||
"当相关系数rho=-0.70时：\n",
|
||
"\t风险系数波动（方差）为：0.0026\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.692307692307692, 投资股票B的份额应为：10w *0.307692307692308\n",
|
||
"当相关系数rho=-0.60时：\n",
|
||
"\t风险系数波动（方差）为：0.0035\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.702702702702703, 投资股票B的份额应为：10w *0.297297297297297\n",
|
||
"当相关系数rho=-0.50时：\n",
|
||
"\t风险系数波动（方差）为：0.0043\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.714285714285714, 投资股票B的份额应为：10w *0.285714285714286\n",
|
||
"当相关系数rho=-0.40时：\n",
|
||
"\t风险系数波动（方差）为：0.0051\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.727272727272727, 投资股票B的份额应为：10w *0.272727272727273\n",
|
||
"当相关系数rho=-0.30时：\n",
|
||
"\t风险系数波动（方差）为：0.0059\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.741935483870968, 投资股票B的份额应为：10w *0.258064516129032\n",
|
||
"当相关系数rho=-0.20时：\n",
|
||
"\t风险系数波动（方差）为：0.0066\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.758620689655172, 投资股票B的份额应为：10w *0.241379310344828\n",
|
||
"当相关系数rho=-0.10时：\n",
|
||
"\t风险系数波动（方差）为：0.0073\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.777777777777778, 投资股票B的份额应为：10w *0.222222222222222\n",
|
||
"当相关系数rho=0.00时：\n",
|
||
"\t风险系数波动（方差）为：0.0080\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.800000000000000, 投资股票B的份额应为：10w *0.200000000000000\n",
|
||
"当相关系数rho=0.10时：\n",
|
||
"\t风险系数波动（方差）为：0.0086\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.826086956521739, 投资股票B的份额应为：10w *0.173913043478261\n",
|
||
"当相关系数rho=0.20时：\n",
|
||
"\t风险系数波动（方差）为：0.0091\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.857142857142857, 投资股票B的份额应为：10w *0.142857142857143\n",
|
||
"当相关系数rho=0.30时：\n",
|
||
"\t风险系数波动（方差）为：0.0096\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.894736842105263, 投资股票B的份额应为：10w *0.105263157894737\n",
|
||
"当相关系数rho=0.40时：\n",
|
||
"\t风险系数波动（方差）为：0.0099\n",
|
||
"\t此时投资股票A的份额应为：10w * 0.941176470588235, 投资股票B的份额应为：10w *0.0588235294117647\n",
|
||
"当相关系数rho=0.50时：\n",
|
||
"\t风险系数波动（方差）为：0.0100\n",
|
||
"\t此时投资股票A的份额应为：10w * 1.00000000000000, 投资股票B的份额应为：10w *0\n",
|
||
"相关系数rho=0.60时，投资方案无实际意义。\n",
|
||
"相关系数rho=0.70时，投资方案无实际意义。\n",
|
||
"相关系数rho=0.80时，投资方案无实际意义。\n",
|
||
"相关系数rho=0.90时，投资方案无实际意义。\n",
|
||
"相关系数rho=1.00时，投资方案无实际意义。\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sympy import *\n",
|
||
"from scipy.stats import norm \n",
|
||
"from sympy.abc import p\n",
|
||
"\n",
|
||
"X = norm(loc=0.1, scale=0.1)\n",
|
||
"Y = norm(loc=0.3, scale=0.2)\n",
|
||
"Dx, Dy = X.var(), Y.var()\n",
|
||
"\n",
|
||
"def compute_risk(Dx, Dy, rho):\n",
|
||
" # print(\"当相关系数rho={:.1f}时：\".format(rho))\n",
|
||
" Cov_xy = rho * sqrt(Dx) * sqrt(Dy)\n",
|
||
" # 目标函数\n",
|
||
" venture = p ** 2 * Dx + (1-p) ** 2 * Dy + 2 * p * (1-p) * Cov_xy\n",
|
||
" # 求驻点\n",
|
||
" venture_dp = diff(venture, p)\n",
|
||
" p0 = solve(venture_dp)\n",
|
||
" # print(\"\\t驻点p0={:.2f}\".format(p0[0]))\n",
|
||
" # 判断在该点是否取得极小值\n",
|
||
" venture_dp_2 = diff(venture_dp, p)\n",
|
||
" temp = venture_dp_2.evalf(subs={p:p0[0]})\n",
|
||
" if temp < 0:\n",
|
||
" print(\"\\t该点不是函数的极小值点。\") \n",
|
||
" venture_min = venture.evalf(subs={p:p0[0]})\n",
|
||
" # print(\"\\t风险系数波动（方差）为：{:.4f}\".format(venture_min))\n",
|
||
" # print(\"\\t此时投资股票A的份额应为：10w * {}, 投资股票B的份额应为：10w *{}\".format(p0[0], 1-p0[0]))\n",
|
||
" return p0[0], venture_min\n",
|
||
"\n",
|
||
"rhos = [-1.0, -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]\n",
|
||
"ps = []\n",
|
||
"ventures = []\n",
|
||
"for rho in rhos:\n",
|
||
" temp1, temp2 = compute_risk(Dx, Dy, rho)\n",
|
||
" ps.append(temp1)\n",
|
||
" ventures.append(temp2)\n",
|
||
"\n",
|
||
"for idx, p in enumerate(ps):\n",
|
||
" r = (idx - 10) * 0.1\n",
|
||
" if (p > 1) or (p < 0):\n",
|
||
" print(\"相关系数rho={:.2f}时，投资方案无实际意义。\".format(r))\n",
|
||
" else:\n",
|
||
" print(\"当相关系数rho={:.2f}时：\".format(r))\n",
|
||
" print(\"\\t风险系数波动（方差）为：{:.4f}\".format(ventures[idx]))\n",
|
||
" print(\"\\t此时投资股票A的份额应为：10w * {}, 投资股票B的份额应为：10w *{}\".format(p, 1-p))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"输出结果为： \n",
|
||
"当相关系数rho=-1.00时：\n",
|
||
"\n",
|
||
"  风险系数波动（方差）为：0.0000 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.666666666666667, 投资股票B的份额应为：10w *0.333333333333333 \n",
|
||
"\n",
|
||
"当相关系数rho=-0.90时： \n",
|
||
"  风险系数波动（方差）为：0.0009 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.674418604651163, 投资股票B的份额应为：10w *0.325581395348837 \n",
|
||
"当相关系数rho=-0.80时： \n",
|
||
"  风险系数波动（方差）为：0.0018 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.682926829268293, 投资股票B的份额应为：10w *0.317073170731707 \n",
|
||
"当相关系数rho=-0.70时： \n",
|
||
"  风险系数波动（方差）为：0.0026 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.692307692307692, 投资股票B的份额应为：10w *0.307692307692308 \n",
|
||
"当相关系数rho=-0.60时： \n",
|
||
"  风险系数波动（方差）为：0.0035 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.702702702702703, 投资股票B的份额应为：10w *0.297297297297297 \n",
|
||
"当相关系数rho=-0.50时： \n",
|
||
"  风险系数波动（方差）为：0.0043 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.714285714285714, 投资股票B的份额应为：10w *0.285714285714286 \n",
|
||
"当相关系数rho=-0.40时： \n",
|
||
"  风险系数波动（方差）为：0.0051 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.727272727272727, 投资股票B的份额应为：10w *0.272727272727273 \n",
|
||
"当相关系数rho=-0.30时： \n",
|
||
"  风险系数波动（方差）为：0.0059 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.741935483870968, 投资股票B的份额应为：10w *0.258064516129032 \n",
|
||
"当相关系数rho=-0.20时： \n",
|
||
"  风险系数波动（方差）为：0.0066 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.758620689655172, 投资股票B的份额应为：10w *0.241379310344828 \n",
|
||
"当相关系数rho=-0.10时： \n",
|
||
"  风险系数波动（方差）为：0.0073 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.777777777777778, 投资股票B的份额应为：10w *0.222222222222222 \n",
|
||
"当相关系数rho=0.00时： \n",
|
||
"  风险系数波动（方差）为：0.0080 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.800000000000000, 投资股票B的份额应为：10w *0.200000000000000 \n",
|
||
"当相关系数rho=0.10时： \n",
|
||
"  风险系数波动（方差）为：0.0086 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.826086956521739, 投资股票B的份额应为：10w *0.173913043478261 \n",
|
||
"当相关系数rho=0.20时： \n",
|
||
"  风险系数波动（方差）为：0.0091 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.857142857142857, 投资股票B的份额应为：10w *0.142857142857143 \n",
|
||
"当相关系数rho=0.30时： \n",
|
||
"  风险系数波动（方差）为：0.0096 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.894736842105263, 投资股票B的份额应为：10w *0.105263157894737 \n",
|
||
"当相关系数rho=0.40时： \n",
|
||
"  风险系数波动（方差）为：0.0099 \n",
|
||
"  此时投资股票A的份额应为：10w * 0.941176470588235, 投资股票B的份额应为：10w *0.0588235294117647 \n",
|
||
"当相关系数rho=0.50时： \n",
|
||
"  风险系数波动（方差）为：0.0100 \n",
|
||
"  此时投资股票A的份额应为：10w * 1.00000000000000, 投资股票B的份额应为：10w *0 \n",
|
||
"相关系数rho=0.60时，投资方案无实际意义。 \n",
|
||
"相关系数rho=0.70时，投资方案无实际意义。 \n",
|
||
"相关系数rho=0.80时，投资方案无实际意义。 \n",
|
||
"相关系数rho=0.90时，投资方案无实际意义。 \n",
|
||
"相关系数rho=1.00时，投资方案无实际意义。 "
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3.10.5 ('.venv': venv)",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.10.5"
|
||
},
|
||
"orig_nbformat": 4,
|
||
"vscode": {
|
||
"interpreter": {
|
||
"hash": "a0798e59729acf8f16dd74a5eaff0380fbaae7e20dddaf23e3973bf13b41dad4"
|
||
}
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 2
|
||
}
|