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Elements of Probability and Statistics(概率論與數(shù)理統(tǒng)計(jì)初步)

Elements of Probability and Statistics(概率論與數(shù)理統(tǒng)計(jì)初步)

出版社:西安電子科技大學(xué)出版社出版時(shí)間:2019-06-01
開本: 23cm 頁(yè)數(shù): 82頁(yè)
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Elements of Probability and Statistics(概率論與數(shù)理統(tǒng)計(jì)初步) 版權(quán)信息

Elements of Probability and Statistics(概率論與數(shù)理統(tǒng)計(jì)初步) 本書特色

教材由概率論與數(shù)理統(tǒng)計(jì)兩部分組成。在概率論部分,要求學(xué)生掌握處理隨機(jī)現(xiàn)象的基本理論與方法,能夠應(yīng)用隨機(jī)變量的概率分布、特別是常見的幾種概率分布的數(shù)學(xué)模型來(lái)解決生產(chǎn)與社會(huì)實(shí)踐中提出的問(wèn)題。在數(shù)理統(tǒng)計(jì)部分要求掌握參數(shù)估計(jì)、假設(shè)檢驗(yàn)的基本理論與方法,為學(xué)生后續(xù)學(xué)習(xí)及實(shí)踐應(yīng)用奠定基礎(chǔ)。主要特點(diǎn)是結(jié)合我校留學(xué)生特點(diǎn),內(nèi)容更有針對(duì)性,更加強(qiáng)調(diào)動(dòng)手能力。

Elements of Probability and Statistics(概率論與數(shù)理統(tǒng)計(jì)初步) 內(nèi)容簡(jiǎn)介

教材由概率論與數(shù)理統(tǒng)計(jì)兩部分組成。在概率論部分,要求學(xué)生掌握處理隨機(jī)現(xiàn)象的基本理論與方法,能夠應(yīng)用隨機(jī)變量的概率分布、特別是常見的幾種概率分布的數(shù)學(xué)模型來(lái)解決生產(chǎn)與社會(huì)實(shí)踐中提出的問(wèn)題。在數(shù)理統(tǒng)計(jì)部分要求掌握參數(shù)估計(jì)、假設(shè)檢驗(yàn)的基本理論與方法,為學(xué)生后續(xù)學(xué)習(xí)及實(shí)踐應(yīng)用奠定基礎(chǔ)。主要特點(diǎn)是結(jié)合我校留學(xué)生特點(diǎn),內(nèi)容更有針對(duì)性,更加強(qiáng)調(diào)動(dòng)手能力。

Elements of Probability and Statistics(概率論與數(shù)理統(tǒng)計(jì)初步) 目錄

Chapter 1 Classical Probability 1 1.1 Sample Space 2 1.2 Event 4 1.3 Counting Sample Points 6 1.3.1 Multiplication Rule 6 1.3.2 Permutations and Combinations 7 1.4 The Concept of Probability 9 1.5 The Axioms of Probability 10 1.6 Some Element Properties on Probability 11 1.7 Assignment of Probabilities 12 1.8 Calculating Probabilities for Unions and Complements 14 1.9 Conditional Probability 16 1.10 Independence 19 1.11 The Law of Total Probability 21 1.12 Bayes Rule 22 Exercises 23 Chapter 2 Discrete Random Variables 28 2.1 Random Variables 28 2.2 Discrete Probability Distribution 29 2.3 Distribution Functions for Random Variables 30 2.4 Expected Values 32 2.5 Functions of a Random Variable 32 2.6 Variance and Standard Deviation 33 Exercises 34 Chapter 3 Continuous Random Variables 37 3.1 Distribution Functions for Continuous Random Variables 38 3.2 Expected Values 39 3.3 Variance 40 3.4 Properties of Expected Values and Variances 41 Exercises 41 Chapter 4 Examples of Random Variables 43 4.1 Binomial Distribution 43 4.2 Properties of Binomial Distributions 44 4.3 Poisson Distributions 44 4.4 The Normal Distribution 45 4.5 Relationships Between Binomial and Normal Distributions 46 Exercises 47 Chapter 5 Descriptive Statistics 50 5.1 Measures of Central Tendency 50 5.2 Measures of Dispersion 52 5.3 StemandLeaf Plot 52 Exercises 54 Chapter 6 Sampling Theory 56 6.1 Sampling 56 6.2 Random Samples, Random Numbers 57 6.3 Population Parameters 57 6.4 Sample Statistics 58 6.5 Sampling Distributions 59 6.6 The Sample Mean 59 6.7 Sampling Distribution of Means 60 6.8 Sampling Distribution of Proportions 61 6.9 Sampling Distribution of Differences and Sums 62 6.10 The Sample Variance 63 Exercises 63 Chapter 7 Estimation 65 7.1 Unbiased Estimates and Efficient Estimates 65 7.2 Point Estimates and Interval Estimates 66 7.3 Method of Moments 66 7.4 Maximum Likelihood Estimators 67 7.5 Confidence Interval Estimates of Population Parameters 70 Exercises 71 Chapter 8 Hypothesis Test 73 8.1 Statistical Hypothesis 73 8.2 Tests of Hypothesis 74 8.3 Type Ⅰ and Type Ⅱ Errors and Level of Significance 75 8.4 Simple and Composite Hypotheses 77 8.5 Testing Hypotheses about the Mean of a Normal Distribution with Known Variance 77 8.6 P Value 79 Exercises 81 Bibliography 82
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Elements of Probability and Statistics(概率論與數(shù)理統(tǒng)計(jì)初步) 作者簡(jiǎn)介

教學(xué):1. 全國(guó)高校數(shù)學(xué)微課程教學(xué)設(shè)計(jì)競(jìng)賽概率論與數(shù)理統(tǒng)計(jì)組華東區(qū)2等獎(jiǎng)(2015); 2. 主持校國(guó)際化課程群《數(shù)據(jù)科學(xué)方法與應(yīng)用國(guó)際化課程群》(2017); 3. 參與校國(guó)際化課程群《數(shù)理基礎(chǔ)課國(guó)際化課程群》(2016); 4. 指導(dǎo)研究生在第三屆全國(guó)應(yīng)用統(tǒng)計(jì)專業(yè)學(xué)位研究生案例大賽中獲三等獎(jiǎng)(2018); 5. 指導(dǎo)研究生全國(guó)數(shù)學(xué)建模獲二等獎(jiǎng)、三等獎(jiǎng)多次(2012-2016)?蒲校1.2017至今主持國(guó)家社會(huì)科學(xué)基金一般項(xiàng)目一項(xiàng); 2.2010.6-2012.6主持完成浙江省自然科學(xué)基金一項(xiàng); 3.2017.4-2018.6 主持完成浙江省統(tǒng)計(jì)局項(xiàng)目一項(xiàng); 4.近五年第一作者完成SCI論文五篇、SSCI論文一篇。教材編寫: 自2012年9月開始主講國(guó)際交流學(xué)院《概率論與數(shù)理統(tǒng)計(jì)》(英)以來(lái),一直堅(jiān)持Elements of Probability and Statistics講義的編寫與完善。至2017年,已主講六次,修改4次。

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