文档介绍：An Introduction to Statistical
Inference and Its Applications
with R
Michael W. Trosset
Department of Statistics
Indiana University
November 10, 2008
I of dice possess the science
and in numbers thus am skilled.
From The Story of Nala, the third book of the Indian epic Mah´
This book is dedicated to
Richard A. Tapia,
my teacher, mentor, collaborator, and friend.
1Translated by H. Milman in 1860. Quoted by Ian Hacking in The Emergence of
Probability, Cambridge University Press, 1975, page 7.
Contents
1 Experiments 7
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Spinning a Penny . . . . . . . . . . . . . . . . . . . . . 8
The Speed of Light . . . . . . . . . . . . . . . . . . . . 9
Termite Foraging Behavior . . . . . . . . . . . . . . . 11
Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . 14
The Importance of Probability . . . . . . . . . . . . . . . . . 17
Games of Chance . . . . . . . . . . . . . . . . . . . . . . . . . 19
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Mathematical Preliminaries 27
Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Probability 45
Interpretations of Probability . . . . . . . . . . . . . . . . . . 45
Axioms of Probability . . . . . . . . . . . . . . . . . . . . . . 46
Finite Sample Spaces . . . . . . . . . . . . . . . . . . . . . . . 55
Conditional Probability . . . . . . . . . . . . . . . . . . . . . 60
Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 72
Case Study: Padrolling in Milton Murayama’s A