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$Basic probability what every math student should know$

Basic probability: what every math student should know

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Bibliographic Details
Main Author:	Tijms, Henk C. 1944- (Author)
Format:	Book
Language:	English
Published:	New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2021]
Edition:	Second edition
Subjects:	Wahrscheinlichkeitstheorie Probabilities / Textbooks Probabilities Textbooks
Online Access:	Inhaltsverzeichnis
Physical Description:	viii, 175 Seiten Diagramme
ISBN:	9789811237492 9811237492 9789811238512 9811238510

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adam_text	Contents Preface v Chapter 1. Combinatorics and Calculus for Probability 1 1.1 Factorials and binomial coefficients........................... 1 1.2 Basic results from calculus.......................................... 7 Chapter 2. Basics of Probability 11 2.1 Foundation of probability.......................................... 12 2.2 The concept of conditional probability..................... 21 2.3 The law of conditional probability ............................... 26 2.4 Bayesian probability.................................................... 29 2.5 The concept of random variable................................. 40 2.6 Expected value and standard deviation..................... 42 2.7 Independent random variables and the squareroot law 51 2.8 Generating functions.................................................... 55 Appendix: Proofs for expected value and variance............ 58 Chapter 3. Useful Probability Distributions 63 3.1 The binomial and hypergeometric distributions.... 63 3.2 The Poisson distribution............................................. 70 3.3 The normal probability density................................. 74 3.4 Central limit theorem and the normal distribution . . 80 3.5 The uniform and exponential probability densities . . 85 3.6 The bivariate normal density.................................... 93 3.7 The chi-square test....................................................... 97 Appendix: Poisson and binomial probabilities......................... 101 vii Contents viii Chapter 4. 4.1 4.2 4.3 4.4 4.5 Real-Life Examples of Poisson Probabilities 103 Fraud in a Canadian lottery..............................................103 Bombs over London in World War II.............................. 105 Winning the lottery twice.................................................107 Santa Claus and a baby whisperer................................. 108 Birthdays and 500 Oldsmobiles........................................110 Chapter 5. Monte Carlo Simulation and Probability 113 5.1 Introduction......................................................................... 113 5.2 Simulation tools ................................................................ 116 5.3 Applications of computer simulation.............................. 123 5.4 Statistical analysis of simulation output........................ 127 Appendix: Python programs for simulation.........................135 Chapter 6. A Primer on Markov Chains 137 6.1 Markov chain model.......................................................... 137 6.2 Absorbing Markov chains.................................................144 6.3 The gambler’s ruin problem..............................................148 6.4 Long-run behavior of Markov chains.............................. 150 6.5 Markov chain Monte Carlo simulation........................... 153 Solutions to Selected Problems 159 Index 173
adam_txt	Contents Preface v Chapter 1. Combinatorics and Calculus for Probability 1 1.1 Factorials and binomial coefficients. 1 1.2 Basic results from calculus. 7 Chapter 2. Basics of Probability 11 2.1 Foundation of probability. 12 2.2 The concept of conditional probability. 21 2.3 The law of conditional probability . 26 2.4 Bayesian probability. 29 2.5 The concept of random variable. 40 2.6 Expected value and standard deviation. 42 2.7 Independent random variables and the squareroot law 51 2.8 Generating functions. 55 Appendix: Proofs for expected value and variance. 58 Chapter 3. Useful Probability Distributions 63 3.1 The binomial and hypergeometric distributions. 63 3.2 The Poisson distribution. 70 3.3 The normal probability density. 74 3.4 Central limit theorem and the normal distribution . . 80 3.5 The uniform and exponential probability densities . . 85 3.6 The bivariate normal density. 93 3.7 The chi-square test. 97 Appendix: Poisson and binomial probabilities. 101 vii Contents viii Chapter 4. 4.1 4.2 4.3 4.4 4.5 Real-Life Examples of Poisson Probabilities 103 Fraud in a Canadian lottery.103 Bombs over London in World War II. 105 Winning the lottery twice.107 Santa Claus and a baby whisperer. 108 Birthdays and 500 Oldsmobiles.110 Chapter 5. Monte Carlo Simulation and Probability 113 5.1 Introduction. 113 5.2 Simulation tools . 116 5.3 Applications of computer simulation. 123 5.4 Statistical analysis of simulation output. 127 Appendix: Python programs for simulation.135 Chapter 6. A Primer on Markov Chains 137 6.1 Markov chain model. 137 6.2 Absorbing Markov chains.144 6.3 The gambler’s ruin problem.148 6.4 Long-run behavior of Markov chains. 150 6.5 Markov chain Monte Carlo simulation. 153 Solutions to Selected Problems 159 Index 173
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spellingShingle	Tijms, Henk C. 1944- Basic probability what every math student should know Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd
subject_GND	(DE-588)4079013-7
title	Basic probability what every math student should know
title_auth	Basic probability what every math student should know
title_exact_search	Basic probability what every math student should know
title_exact_search_txtP	Basic probability what every math student should know
title_full	Basic probability what every math student should know Henk Tijms
title_fullStr	Basic probability what every math student should know Henk Tijms
title_full_unstemmed	Basic probability what every math student should know Henk Tijms
title_short	Basic probability
title_sort	basic probability what every math student should know
title_sub	what every math student should know
topic	Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd
topic_facet	Wahrscheinlichkeitstheorie
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