كتاب Introduction to Probability

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Introduction to Probability
Charles M. Grinstead
Swarthmore College

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Contents
1 Discrete Probability Distributions 1
1.1 Simulation of Discrete Probabilities . 1
1.2 Discrete Probability Distributions 18
2 Continuous Probability Densities 41
2.1 Simulation of Continuous Probabilities . 41
2.2 Continuous Density Functions 55
3 Combinatorics 75
3.1 Permutations . 75
3.2 Combinations . 92
3.3 Card Shuffling . 120
4 Conditional Probability 133
4.1 Discrete Conditional Probability 133
4.2 Continuous Conditional Probability . 162
4.3 Paradoxes . 175
5 Distributions and Densities 183
5.1 Important Distributions . 183
5.2 Important Densities . 205
6 Expected Value and Variance 225
6.1 Expected Value 225
6.2 Variance of Discrete Random Variables . 257
6.3 Continuous Random Variables 268
7 Sums of Random Variables 285
7.1 Sums of Discrete Random Variables 285
7.2 Sums of Continuous Random Variables . 291
8 Law of Large Numbers 305
8.1 Discrete Random Variables . 305
8.2 Continuous Random Variables 316
vvi CONTENTS
9 Central Limit Theorem 325
9.1 Bernoulli Trials 325
9.2 Discrete Independent Trials . 340
9.3 Continuous Independent Trials . 356
10 Generating Functions 365
10.1 Discrete Distributions 365
10.2 Branching Processes . 376
10.3 Continuous Densities . 393
11 Markov Chains 405
11.1 Introduction 405
11.2 Absorbing Markov Chains 416
11.3 Ergodic Markov Chains . 433
11.4 Fundamental Limit Theorem 447
11.5 Mean First Passage Time 452
12 Random Walks 471
12.1 Random Walks in Euclidean Space . 471
12.2 Gambler’s Ruin 486
12.3 Arc Sine Laws

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