文档介绍：Instructor's Solutions Manual
Third Edition
Fundamentals of
ProbabilitY
With Stochastic Processes
SAEED GHAHRAMANI
Western New England College
Upper Saddle River, New Jersey 07458
Contents
1 Axioms of Probability 1
Sample Space and Events 1
Basic Theorems 2
Random Selection of Points from Intervals 7
Review Problems 9
binatorial Methods 13
Counting Principle 13
Permutations 16
18
Stirling’ Formula 31
Review Problems 31
3 Conditional Probability and Independence 35
Conditional Probability 35
Law of Multiplication 39
Law of Total Probability 41
Bayes’ Formula 46
Independence 48
Applications of Probability to ics 56
Review Problems 59
Distribution Functions and
4 63
Discrete Random Variables
Distribution Functions 63
Discrete Random Variables 66
Expectations of Discrete Random Variables 71
Variances and Moments of Discrete Random Variables 77
Standardized Random Variables 83
Review Problems 83
iv Contents
5 Special Discrete Distributions 87
Bernoulli and Binomial Random Variables 87
Poisson Random Variable 94
Other Discrete Random Variables 99
Review Problems 106
6 Continuous Random Variables 111
Probability Density Functions 111
Density Function of a Function of a Random Variable 113
Expectations and Variances 116
Review Problems 123
7 Special Continuous Distributions 126
Uniform Random Variable 126
Normal Random Variable 131
Exponential Random Variables 139
Gamma Distribution 144
Beta Distribution 147
Survival Analysis and Hazard Function 152
Review Problems 153
8 Bivariate Distributions 157
Joint Distribution of Two Random Variables 157
Independent Random Variables 166
Conditional Distributions 174
Transformations of Two Random Variables 183
Review Problems 191
9 Multivariate Distributions 2