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1、概率论与数理统计Probability theory and mathematical statistics第一早随机事件与概率Ch apter 1. Ran dom events and probability试验 Experime nt随机的Random;Stochastic随机性 Randomness随机试验Randomtest; Random experiment随机事件Randomevent基本事件Elementaryevent复合事件 Compoundevent样本空间Samplespace必然事件Certainevent不可能事件Impossibleevent事件的出现Occur
2、re nee of event积事件Productevent不相容 In compatible互不相容Mutuallyexclusive不相容事件In compatibleevent不相交事件Disjionteven ts频率 Freque ncy概率 Probability可能性 Possibility不可数集 Non-denumerableset; Non-enumerable set可数的Numerable可列 Cou ntable;Denumerable; Enumerable可列无穷Enumerableinfinite可列可加性Countableadditivity概率模型 Prob
3、abilisticmodel等概率Equalprobability等可能事件Equally likely eve nt条件概率Conditionalprobability乘法定理 Multiplicationtheorem乘积公式Productformula全概率Totalprobability贝叶斯定理Bayes'Theorem后验概率Posteriorprobability先验概率Priorprobability独立 In depe ndence独立事件Independenteve nt独立随机事件In depe ndent ran dom event两两独立Pairwisein
4、depe ndence两两独立事件Pairwise in depe ndence eve nts伯努利试验Bernouill ' strial事件序列Sequeneeof eve nts第一早 随机变量及其分布Chapter 2. Ran dom variables and their distributi on2分布 Distributio n概率分布Probabilitydistributi on随机变量Randomvariable离散 Discrete离散随机变量Discrete ran dom variable离散分布Discretedistributi on一维概率分布 On
5、 e-dime nsio nalprobability distribution连续随机变量Continuous random variable连续分布Continuousdistributi on密度函数Densityfun cti on分布函数Distributionfun cti on两点分布Two-pointdistributi on零一分布Zero-onedistributi on二项分布Bi no mialdistributi on超几何分布 Hypergeometrydistributi on泊松分布Poissondistributi on均匀分布Uniformdistribut
6、i on指数分布Exponentialdistributi on正态分布Normaldistributi on咼斯分布Gaussiandistributi on标准正态分布Standardno rmal distributi on几何分布Geometricdistributi on吩布Gammadistributi on瑞利分布Rayleighdistributi on第一早 二维随机变量及其分布Chapter 3. Two-dimension random variables and their distribution随机向量 Randomvector联合分布Joi ntdistribut
7、i onn维概率分布n-dime nsional probability distributi on边缘分布Marginaldistributi on联合分布函数Joint distributi on function联合概率分布Joint probability distribution条件概率分布Con ditio nalprobability distribution条件概率函数Con diti onal probability function联合密度Joi ntden sity联合概率密度Joint probability den sity边缘密度Marginalden sity条件
8、概率密度Conditionalprobability density二元正态分布Bivariate no rmal distributio n多元正态分布Multivariateno rmal distributi on多维正态分布Multidime nsional no rmal distributi onn维正态分布n-dime nsional no rmal distributi on随机变量独立性In depe ndence of ran dom variable独立随机变量In depe ndent ran dom variable卷积 Con voluti on第四早 数子特征Ch
9、apter 4. Numeric characteristic期望 Expectati on数学期望Mathematicalexpectati on均值向量Meanvector方差 Varia nee标准差Standarddeviati on偏差 Deviati on标准化随机变量Stan dardized ran dom variable协方差 Covarianee协方差矩阵Covarianeematrix相关系数Correlationcoefficient ; Related coefficient不相关 Irrelevanee负相关Negativecorrelati on矩 Mome n
10、t中心矩Centralmome nt一阶矩Firstmome nt峰度 Leptokurtosis矩函数Momentfunction矩母函数Mome nt gen erati ng function切比雪夫不等式 Chybyshevin equality依概率收敛Con verge neein probability弱收敛Weakeon verge nee大数疋律Law of large nu mber弱大数定律Weak law of large nu mbers中心极限定理Ce ntrallimit Theorem极限分布Limitingdistributi on第五早 数理统计的基本概念C
11、hapter 5. Fun dame ntal con cept of mathematical statistics统计 Statistic总体 Population;Ensemble; Totality总体分布Populationdistributi on总体参数Populationparameter随机抽样法Method of ran dom sampli ng数据处理Dataprocessi on观测值Observedvalue组距Classin terval组限Classlimits组平均Classmea n组中值Classmidpoi nt分组误差Groupingerror直方图H
12、istogram经验方差Empiricalvaria nee经验分布函数Empiricaldistribution function正态总体Normalpopulati on简单平均Simpleaverage平均值Mean;Mean value; Average权 Weight加权平均值Weightedaverage; Weighted mean总体均值Populationmean； Ensemble average总体方差Populationvaria nee离差平方和Sum of squares of deviati ons总体矩 Populationmome nt总体中心矩Populat
13、ioncen tral mome nt样本Sample样本均值Sampleaverage样本相关系数Samplecorrelati on coefficie nt样本均值Samplemea n样本矩Samplemome nt样本点Samplepoi nt样本容量Samplesize样本空间Samplespace样本标准差Sample sta ndard deviati on样本方差Samplevaria nee抽样 Sampli ng抽样检验Samplingin spect ion均方根 Root-mean-square均方差Meansquare deviati on众数Mode分位数Quan
14、tile峰值Peakx2分布Chi square distributi ont 分布 t-distributi on临界值Marginalvalue自由度Degreeof freedom无限自由度Infin ite degree of freedom充分统计量Sufficientstatistics第六早 参数估计Chapter 6. Parameter estimation总体参数Parameter of populati on估计 Estimate估计量Estimator点估计Pointestimati on矩法Method of mome nt矩估计法Momentmethod of es
15、timati on似然函数Likelihoodfun ctio n似然方程Likelihoodequati on最大似然Maximumlikelihood最大似然法Method of maximum likelihood最大似然估计 Maximumlikelihood estimate相关的估计量Estimate of correlati on充分估计量Sufficientestimates无偏的Un biased无偏性 Un biased ness;Without bias无偏估计Un biasedestimate; Un biased estimati on有效性Validity有效估计E
16、fficiencyestimati on有效估计量 Efficiencyestimator均方误差Meansquare error最小方差估计Minimum variance estimation一致取小方差无偏估计Uniformly minimum variance unbiased estimation区间估计Intervalestimation ； Estimate by a interval置信区间Confideneeinterval; Fiducial interval置信水平Confideneelevel置信度Degreeof con fide nce置信限Fiduciallimi
17、t总体比例估计Estimate of population proportion总体方差估计Estimate of population variance第七早 假设检验Chapter 7.Hypothesis testing假设 Hypothesis统计假设Statisticalhypothesis假设检验Hypothesistest ing; Test of hypothesis; Testi ng of hypothesis小概率事件Event of small probability检验统计量Teststatistics双侧检验Two-sidestest接受域Regionof acce
18、ptance; Acceptance region拒绝域Regi on of reject ion显著水平Level of significance ; Significance level第八早 回归分析Chapter 8. Regressi on an alysis回归 Regressio n回归分析 Regressionan alysis回归方程Regressionequatio n回归系数估计Estimate of regressi on coefficie nt线性回归Lin earregressi on拟和 Fitti ng最小一乘法Leastsquare method ; Minimum squares method残差 Residual残差平方和Residual sum of squares; Square sum of residues方差分析 Varianeean alysis曲线拟和Fitt ing of a curve多项式拟和Fitt ing of a polyno mial直线拟和Fitt ing of a straight li ne拟和优度Goodnessof fit拟和优度检验Good ness of fit test非线性回归Nonlinearregressi on非线性回归分析 Nonlin earregressi on an alysis7