隨機(jī)數(shù)學(xué)及其應(yīng)用

書籍目錄

Chapter 1  Events and Probability  1.1 Events as Sets  1.2 Probability  1.3 ExercisesChapter 2  Random Variables and Their Distributions  2.1 Random Variables  2.2 Discrete Random Variables  2.3 Expected Value of Discrete Random Variable  2.4 Expectation of a Function of a Discrete Random Variable  2.5 Variance of Random Variables  2.6 Continuous Random Variables  2.7 Distribution of a Function of a Random Variable  2.8 ExercisesChapter 3  Joint Distributions of Two Random Variables  3.1 Joint Cumulative Probability Distribution Function  3.2 Joint Probability Mass Function for Discrete Random Variable ...  3.3 Joint Probability Density Function  3.4 Independent Random Variables  3.5 Covariance  3.6 Correlation Coefficient  3.7 Bivariate Normal Distribution  3.8 Conditional Distributions  3.9 Joint Probability Distribution of Functions of Random Variables  3.10 ExercisesChapter 4  Law of Large Numbers  4.1 Generating Functions and Their Applications  4.2 Characteristic Functions  4.3 Limit Theorems  4.4 Law of Large Numbers (LLN)  4.5 ExercisesChapter 5  Mathematical Statistics  5.1 Introduction  5.2 Random Sampling  5.3 Distributions of Statistics  5.4 The Sample Mean and the Sample Variance  5.5 Point Estimation  5.6 Confidence Intervals  5.7 Testing of Hypotheses  5.8 ExercisesChapter 6  Approaches to Semiparametric Bounds on Means and Variances  6.1 Introduction to Moment Problems  6.2 Convex Optimization Approach(Duality Theory)  6.3 Semidefinite Programming(SDP)  6.4 Khinchin Transform Method for Unimodal Distributions  6.5 Convex Representation  6.6 Symmetrization Methods for Variance  6.7 Optimal Distance and Optimal Ratio  6.8 Other MethodsIndex

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劉國(guó)慶、艾曉輝主編的《隨機(jī)數(shù)學(xué)及其應(yīng)用》涉及隨機(jī)事件、概率公理、全概率公式、貝葉斯公式、隨機(jī)變量及其分布、二維變量的聯(lián)合分布、數(shù)學(xué)期望、條件期望、大數(shù)定律、數(shù)理統(tǒng)計(jì)等內(nèi)容。本書提供了處理截尾變量均值與方差的半?yún)?shù)界的方法。本書可為廣大讀者在概率論、高斯過(guò)程、小值概率、Stein方法、矩問(wèn)題等領(lǐng)域進(jìn)一步學(xué)習(xí)提供必要的知識(shí)儲(chǔ)備。

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