Probability Models Book

1	Probability Spaces	1
	The Idea of Probability	2
	Laws of Probability	3
	Consequences	5
	Equally Likely Outcomes	10
	The Continuous Version	16
	Intellectual Honesty	21
2	Conditional Probability and Independence	23
	Conditional Probability	23
	Bayes' Theorem	31
	Independence	36
	The Borel-Cantelli Lemmas	43
3	Common Probability Distributions	45
	Common Discrete Probability Spaces	45
	Probability Generating Functions	53
	Common Continuous Probability Spaces	54
	Mixed Probability Spaces	59
4	Random Variables	61
	The Definition	62
	Discrete Random Variables	63
	Continuous Random Variables	72
	Jointly Distributed Random Variables	75
	Conditional Expectation	88
5	Sums of Random Variables	93
	Discrete Variables	93
	General Random Variables	100
	Records	113
6	Convergence and Limit Theorems	117
	Inequalities	118
	Convergence	121
	Limit Theorems	129
7	Stochastic Processes in Discrete Time	139
	Branching Processes	140
	Random Walks	145
	Markov Chains	155
8	Stochastic Processes in Continuous Time	169
	Markov Chains in Continuous Time	169
	Queues	186
	Renewal Theory	200
	Brownian Motion: The Wiener Process	210
9	Appendix: Common Distributions and Mathematical Facts	223
	Discrete Distributions	223
	Continuous Distributions	224
	Miscellaneous Mathematical Facts	225
	Bibliography	227
	Solutions	229
	Index	253