文档介绍：Introduction to Probability
Charles M. Grinstead
Swarthmore College
J. Laurie Snell
Dartmouth College
To our wives
and in memory of
Reese T. Prosser
Contents
1 Discrete Probability Distributions 1
Simulation of Discrete Probabilities . . . . . . . . . . . . . . . . . . . 1
Discrete Probability Distributions . . . . . . . . . . . . . . . . . . . . 18
2 Continuous Probability Densities 41
Simulation of Continuous Probabilities . . . . . . . . . . . . . . . . . 41
Continuous Density Functions . . . . . . . . . . . . . . . . . . . . . . 55
binatorics 75
Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Card Shuffling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4 Conditional Probability 133
Discrete Conditional Probability . . . . . . . . . . . . . . . . . . . . 133
Continuous Conditional Probability . . . . . . . . . . . . . . . . . . . 162
Paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5 Distributions and Densities 183
Important Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 183
Important Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
6 Expected Value and Variance 225
Expected Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Variance of Discrete Random Variables . . . . . . . . . . . . . . . . . 257
Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . 268
7 Sums of Random Variables 285
Sums of Discrete Random Variables . . . . . . . . . . . . . . . . . . 285
Sums of Continuous Random Variables . . . . . . . . . . . . . . . . . 291
8 Law of Large Numbers 305
Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . 305
Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . 316
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