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概率论与数理统计ProbabilityTheoryandMathematicalStatistics第一章概率论的基本概念Chapter1IntroductionofProbabilityTheory不确定性indeterminacy必然现象certainphenomenon随机现象randomphenomenon试验experiment结果outcome频率数frequencynumber样本空间samplespace出现次数frequencyofoccurrencen维样本空间n-dimensionalsamplespace样本空间的点pointinsamplespace随机事件randomevent/randomoccurrence基本事件elementaryevent必然事件certainevent不可能事件impossibleevent等可能事件equallylikelyevent事件运算律operationalrulesofevents事件的包含implicationofevents并事件unionevents交事件intersectionevents互不相容事件、互斥事件mutuallyexclusiveevents//incompatibleevents互逆的mutuallyinverse加法定理additiontheorem古典概率classicalprobability古典概率模型classicalprobabilisticmodel几何概率geometricprobability乘法定理producttheorem概率乘法multiplicationofprobabilities条件概率conditionalprobability全概率公式、全概率定理formulaoftotalprobability贝叶斯公式、逆概率公式Bayesformula后验概率posteriorprobability先验概率priorprobability独立事件independentevent独立随机事件independentrandomevent独立实验independentexperiment两两独立pairwiseindependent两两独立事件pairwiseindependentevents第二章随机变量及其分布Chapter2RandomVariablesandDistributions随机变量randomvariables离散随机变量discreterandomvariables概率分布律lawofprobabilitydistribution一维概率分布one-dimensionprobabilitydistribution概率分布probabilitydistribution两点分布two-pointdistribution伯努利分布Bernoullidistribution二项分布/伯努利分布Binomialdistribution超几何分布hypergeometricdistribution三项分布trinomialdistribution多项分布polynomialdistribution泊松分布Poissondistribution泊松参数Poissontheorem分布函数distributionfunction概率分布函数probabilitydensityfunction连续随机变量continuousrandomvariable概率密度probabilitydensity概率密度函数probabilitydensityfunction概率曲线probabilitycurve均匀分布uniformdistribution指数分布exponentialdistribution指数分布密度函数exponentialdistributiondensityfunction正态分布、高斯分布normaldistribution标准正态分布standardnormaldistribution正态概率密度函数normalprobabilitydensityfunction正态概率曲线normalprobabilitycurve标准正态曲线standardnormalcurve柯西分布Cauchydistribution分布密度densityofdistribution第三章多维随机变量及其分布Chapter3MultivariateRandomVariablesandDistributions二维随机变量two-dimensionalrandomvariable联合分布函数jointdistributionfunction二维离散型随机变量two-dimensionaldiscreterandomvariable二维连续型随机变量two-dimensionalcontinuousrandomvariable联合概率密度jointprobabilityvariablen维随机变量n-dimensionalrandomvariablen维分布函数n-dimensionaldistributionfunctionn维概率分布n-dimensionalprobabilitydistribution边缘分布marginaldistribution边缘分布函数marginaldistributionfunction边缘分布律lawofmarginaldistribution边缘概率密度marginalprobabilitydensity二维正态分布two-dimensionalnormaldistribution二维正态概率密度two-dimensionalnormalprobabilitydensity第四章随机变量的数字特征Chapter4NumericalCharacteristicsofRandomVariables数学期望、均值mathematicalexpectation期望值expectationvalue方差variance标准差standarddeviation随机变量的方差varianceofrandomvariables均方差meansquaredeviation相关关系dependencerelation相关系数correlationcoefficient协方差covariance协方差矩阵covariancematrix切比雪夫不等式Chebyshevinequality第五章大数定律及中心极限定理Chapter5LawofLargeNumbersandCentralLimitTheorem大数定律lawofgreatnumbers切比雪夫定理的特殊形式specialformofChebyshevtheorem依概率收敛convergenceinprobability伯努利大数定律Bernoullilawoflargenumbers同分布samedistribution列维-林德伯格定理、独立同分布中心极限定理independentLevy-Lindbergtheorem辛钦大数定律Khinchinelawoflargenumbers利亚普诺夫定理Liapunovtheorem棣莫弗-拉普拉斯定理DeMoivre-Laplacetheorem