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| 內容簡介: |
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本书包括随机事件与概率、一维随机变量及其分布、多维随机变量及其分布、随机变量的数字特征、大数定律及中心极限定理,统计量及其分布、参数估计、假设检验等内容。每一章有章节思维导图,每节后面附有相应的习题及部分考研真题。本书可作为高等学校理工科、经济类、管理类和其他非数学专业教学用书,也适合数学专业专科的概率论与数理统计课程的教学需要。
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| 關於作者: |
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赵军圣,聊城大学数学科学学院副院长、副教授,山东省大数据教学指导委员会副秘书长,主要研究方向为人工智能与模式识别。
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| 目錄:
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第一章 随机事件与概率···········································································································1 第一节 随机事件及其运算·································································································1 一、随机试验与样本空间 ··································································································1 二、随机事件 ··················································································································2 三、随机事件的关系与运算 ······························································································3 习题 1.1 ···························································································································6 第二节 随机事件的概率 ····································································································7 一、古典概型 ··················································································································8 二、几何概型 ················································································································10 三、频率与概率 ·············································································································12 四、概率的公理化定义及其运算性质 ···············································································13 习题 1.2 ·························································································································16 第三节 条件概率与全概率公式·······················································································17 一、条件概率 ················································································································17 二、乘法定理 ················································································································19 三、全概率公式与贝叶斯公式 ·························································································20 习题 1.3 ·························································································································23 第四节 随机事件的独立性·······························································································25 习题 1.4 ·························································································································28 第五节 伯努利概型··········································································································29 习题 1.5 ·························································································································32 第一章思维导图··················································································································33 第二章 随机变量及其概率分布····························································································34 第一节 随机变量的定义 ··································································································34 习题 2.1 ·························································································································36 第二节 离散型随机变量及其概率分布 ···········································································36 一、两点分布(0-1 分布) ·································································································37 二、二项分布 ················································································································38 三、泊松分布 ················································································································40 四、超几何分布 ·············································································································42 概率论与数理统计 6 五、几何分布 ················································································································44 习题 2.2 ·························································································································45 第三节 随机变量的分布函数···························································································46 习题 2.3 ·····························································································
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