Basic probability: what every math student should know
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2021]
|
| Ausgabe: | Second edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 175 Seiten Diagramme |
| ISBN: | 9789811237492 9811237492 9789811238512 9811238510 |
Internformat
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Datensatz im Suchindex
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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
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| 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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| index_date | 2024-07-03T18:00:10Z |
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| isbn | 9789811237492 9811237492 9789811238512 9811238510 |
| language | English |
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| publishDate | 2021 |
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| spellingShingle | Tijms, Henk C. 1944- Basic probability what every math student should know Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
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| 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 |
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| 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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Inhaltsverzeichnis
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 800 T568(2) |
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| Exemplar 1 | ausleihbar Verfügbar Bestellen |