文档介绍：CSSS 2000–2001 Math Review Lectures:
Probability, Statistics and Stochastic Processes
Cosma Rohilla Shalizi
University of Wisconsin-Madison, Physics Department, and the Santa Fe Institute
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Presented 4 June 2000
and 11 June 2001
2
i
These notes are available electronically from /∼shalizi/prob-notes/.
Reports of typos, and more serious bugs, are eagerly requested.
Revision History
ments
4 June 2000 First version finished (about four hours before teaching from it).
8 July 2000 Minor typo fixes, some points amplified in response to ments;
added list of deficiencies as Appendix B.
11 June 2001 More typo fixes, added paragraph on large deviation principle, second presentation.
14 July 2001 Fixed two errors (thanks to Cecile Viboud and Antonio Ramirez)
Contents
Part I: Probability 1
1 What’s a Probability Anyway? 1
2 Probability Calculus 2
Basic Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
A Caution about Probabilities 0 and 1 . . . . . . . . . . . 3
Conditional Probabilities . . . . . . . . . . . . . . . . . . . . . . . 3
3 Random Variables 5
Properties of Random Variables . . . . . . . . . . . . . . . . . . . 6
Functions of Random Variables . . . . . . . . . . . . . . . 6
Multiple Random Variables; Independence . . . . . . . . . 6
Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Expectations of Multiple Variables . . . . . . . . . . . . . 7
Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Particularly Important Moments . . . . . . . . . . . . . . 8
Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Variance and Standard Deviation . . . . . . . . . . . . . . 8
4 Important Discrete Distributions 9
The Bernoulli Distribution . . . . . . . . . . . . . . . . . . . . . . 9
The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . 9
The Poisson