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1、概率论与数理统计Probabilitytheoryandmathematicalstatistics第一章随机事件与概率Chapter1.Randomeventsandprobability试验Experiment随机的Random；Stochastic随机性Randomness随机试验Randomtest；Randomexperiment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Occurrenceofevent积事件Pr
2、oductevent不相容Incompatible互不相容Mutuallyexclusive不相容事件Incompatibleevent不相交事件Disjiontevents频率Frequency概率Probability可能性Possibility不可数集Non-denumerableset；Non-enumerableset可数的Numerable可列Countable；Denumerable；Enumerable可列无穷Enumerableinfinite可列可加性Countableadditivity概率模型Probabilisticmodel等概率Equalprobability等可
3、能事件Equallylikelyevent条件概率Conditionalprobability乘法定理Multiplicationtheorem乘积公式Productformula全概率Totalprobability贝叶斯定理BayesTheorem后验概率Posteriorprobability先验概率Priorprobability独立Independence独立事件Independentevent独立随机事件Independentrandomevent两两独立Pairwiseindependence两两独立事件Pairwiseindependenceevents伯努利试验Bernoui
4、llstrial事件序列Sequenceofevents第二章随机变量及其分布Chapter2.Randomvariablesandtheirdistribution#分布Distribution概率分布Probabilitydistribution随机变量Randomvariable离散Discrete离散随机变量Discreterandomvariable离散分布Discretedistribution一维概率分布One-dimensionalprobabilitydistribution连续随机变量Continuousrandomvariable连续分布Continuousdistrib
5、ution密度函数Densityfunction分布函数Distributionfunction两点分布Two-pointdistribution零一分布Zero-onedistribution二项分布Binomialdistribution超几何分布Hypergeometrydistribution泊松分布Poissondistribution均匀分布Uniformdistribution指数分布Exponentialdistribution正态分布Normaldistribution高斯分布Gaussiandistribution标准正态分布Standardnormaldistributi
6、on几何分布Geometricdistributionr分布Gammadistribution瑞利分布Rayleighdistribution弟早一维随机变里及其分布hapter3.Two-dimensionrandomvariablesandtheirdistribution随机向量Randomvector联合分布Jointdistributionn维概率分布n-dimensionalprobabilitydistribution边缘分布Marginaldistribution联合分布函数Jointdistributionfunction联合概率分布Jointprobabilitydistr
7、ibution条件概率分布Conditionalprobabilitydistribution条件概率函数Conditionalprobabilityfunction联合密度Jointdensity联合概率密度Jointprobabilitydensity边缘密度Marginaldensity条件概率密度Conditionalprobabilitydensity一元正态分布Bivariatenormaldistribution多元正态分布Multivariatenormaldistribution多维正态分布Multidimensionalnormaldistributionn维正态分布n-d
8、imensionalnormaldistribution随机变量独立性Independenceofrandomvariable独立随机变量Independentrandomvariable卷积Convolution#第四章数字特征Chapter4.Numericcharacteristic期望Expectation数学期望Mathematical均值向量Mean方差Variance标准差Standard偏差Deviation标准化随机变量协方差Covariance协方差矩阵Covariance相关系数Correlation不相关Irrelevance负相关Negative矩Moment中心矩C
9、entral一阶矩First峰度Leptokurtosis矩函数Moment矩母函数切比雪夫不等式Chybyshev依概率收敛Convergence弱收敛Weak大数定律弱大数定律中心极限定理Central极限分布LimitingexpectationvectordeviationStandardizedrandomvariablematrixcoefficient；RelatcorrelationmomentmomentfunctionMomentgeneratingfunctioninequalityinprobabilityconvergenceLawoflargenumberWeakl
10、awoflargenumberslimitTheoremdistribution第五章数理统计的基本概念Chapter5.Fundamentalconceptofmathematicalstatistics统计Statistic#第四章数字特征Chapter4.Numericcharacteristic；Ensemble；TotalitydistributionparameterMethodofrandomsamplingprocessionvalueintervallimitsmeanmidpointerrorvariancedistributionfunctionpopulation总体P
11、opulation总体分布Population总体参数Population随机抽样法数据处理Data观测值Observed组距Class组限Class组平均Class组中值Class分组误差Grouping直方图Histogram经验方差Empirical经验分布函数Empirical正态总体Normal#第四章数字特征Chapter4.Numericcharacteristic#average；Meanvalue；Averageaverage；Weightedmeanmean；EnsembleaveragevarianceSumofsquaresofdeviationsmomentcentr
12、almomentaveragecorrelationcoefficientmeanmomentpointsizespaceSamplestandarddeviationvarianceinspectionsquaredeviation简单平均Simple平均值Mean权Weight加权平均值Weighted总体均值Population总体方差Population离差平方和总体矩Population总体中心矩Population样本Sample样本均值Sample样本相关系数Sample样本均值Sample样本矩Sample样本点Sample样本容量Sample样本空间Sample样本标准差样本
13、方差Sample抽样Sampling抽样检验Sampling均方根Root-mean-square均方差Mean众数Mode分位数Quantile峰值PeakX2分布t分布t-distribution临界值Marginal自由度Degree无限自由度充分统计量SufficientChisquaredistributionvalueoffreedomInfinitedegreeoffreedomstatistics#第六章参数估计Chapter6.Parameterestimation#ParameterofpopulationestimationMethodofmomentmethodofes
14、timationfunctionequationlikelihoodMethodofmaximumlikelihoodlikelihoodestimate总体参数估计Estimate估计量Estimator点估计Point矩法矩估计法Moment似然函数Likelihood似然方程Likelihood最大似然Maximum最大似然法最大似然估计Maximum#相关的估计量充分估计量Sufficient无偏的Unbiased无偏性Unbiasedness无偏估计UnbiasedEstimateofcorrelationestimates；Withoutbiasestimate；Unbiasedestimation有效性Validity有效估计Efficiency有效估计量Efficiency均方误差Mean最小方差估计一致最小方差无偏估计区间估计Interval置信区间Confidence置信水平Confidence置信度Degree置信限Fiducial总体比例估计总体方差估计estimationestimatorsquareerrorMinimumvarianceestimationUniformlyminimumvarian
