From c201670574d8c490822753d84f9d8349ca7af114 Mon Sep 17 00:00:00 2001 From: bingyi Date: Mon, 27 Oct 2025 20:34:53 +0800 Subject: [PATCH] =?UTF-8?q?=E5=A2=9E=E5=8A=A0README=E6=96=87=E4=BB=B6?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 90 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ book.jpg | Bin 0 -> 473713 bytes 2 files changed, 90 insertions(+) create mode 100644 README.md create mode 100644 book.jpg diff --git a/README.md b/README.md new file mode 100644 index 0000000..c34e17e --- /dev/null +++ b/README.md @@ -0,0 +1,90 @@ +# 概率论与数理统计 + +书中定理和例子的不跳步骤的完整证明 + +## 书籍信息 +- **书名**: 概率论与数理统计 +- **封面**: ![book cover](book.jpg) + +## 内容简介 +本教材系统介绍了概率论与数理统计的基本理论、方法及其应用。内容涵盖从基础的随机事件与概率到高级的统计推断方法,为学习统计学、数据科学及相关领域提供了坚实的数学基础。 + +## 目录结构 + +### 前辅文 + +### 第一章 随机事件与概率 +- §1.1 随机事件及其运算 + - 随机现象、样本空间、随机事件 + - 随机变量、事件关系与运算 + - 事件域 +- §1.2 概率的定义及其确定方法 + - 概率公理化定义 + - 排列组合、频率方法、古典方法 + - 几何方法、主观方法 +- §1.3 概率的性质 + - 可加性、单调性、加法公式、连续性 +- §1.4 条件概率 + - 条件概率定义、乘法公式 + - 全概率公式、贝叶斯公式 +- §1.5 独立性 + - 事件独立性、试验独立性 + +### 第二章 随机变量及其分布 +- §2.1 随机变量及其分布 + - 随机变量概念、分布函数 + - 离散与连续随机变量的概率分布 +- §2.2 随机变量的数学期望 + - 期望概念、定义与性质 +- §2.3 随机变量的方差与标准差 + - 方差定义、性质、切比雪夫不等式 +- §2.4 常用离散分布 + - 二项分布、泊松分布、超几何分布 + - 几何分布与负二项分布 +- §2.5 常用连续分布 + - 正态分布、均匀分布、指数分布 + - 伽马分布、贝塔分布 +- §2.6 随机变量函数的分布 +- §2.7 分布的其他特征数 + - k阶矩、变异系数、分位数 + - 中位数、偏度系数、峰度系数 + +### 第三章 多维随机变量及其分布 +- §3.1 多维随机变量及其联合分布 +- §3.2 边际分布与随机变量的独立性 +- §3.3 多维随机变量函数的分布 +- §3.4 多维随机变量的特征数 + - 协方差、相关系数 + - 期望向量与协方差矩阵 +- §3.5 条件分布与条件期望 + +### 第四章 大数定律与中心极限定理 +- §4.1 随机变量序列的两种收敛性 +- §4.2 特征函数 +- §4.3 大数定律 +- §4.4 中心极限定理 + +### 第五章 统计量及其分布 +- §5.1 总体与样本 +- §5.2 样本数据的整理与显示 +- §5.3 统计量及其分布 + - 样本均值、方差、矩函数 + - 次序统计量、分位数、箱线图 +- §5.4 三大抽样分布 + - χ²分布、F分布、t分布 +- §5.5 充分统计量 + +### 第六章 参数估计 +- §6.1 点估计的概念与无偏性 +- §6.2 矩估计及相合性 +- §6.3 最大似然估计与EM算法 +- §6.4 最小方差无偏估计 +- §6.5 贝叶斯估计 +- §6.6 区间估计 + +### 第七章 假设检验 +- §7.1 假设检验的基本思想与概念 +- §7.2 正态总体参数假设检验 +- §7.3 其他分布参数的假设检验 +- §7.4 似然比检验与分布拟合检验 +- 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