文档介绍：An Introduction to Statistical
Inference and Its Applications
Michael W. Trosset
Department of Mathematics
College of William & Mary
January 5, 2005
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´abarata.
This book is dedicated to
Richard A. Tapia,
my teacher, mentor, collaborator, and friend.
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 All I asking
for is my body . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Exercises . . . . . . . . . . . . . . . . . .