Solution Manual For Fundamentals of Probability With Stochastic Processes, 3rd Edition By Saeed Ghahramani

, Instructor's Solutions Manual




Third Edition

Fundamentals of
ProbabilitY
With Stochastic Processes




SAEED GHAHRAMANI
Western New England College




Upper Saddle River, New Jersey 07458

,
, C ontents

1 Axioms of Probability 1

1.2 Sample Space and Events 1
1.4 Basic Theorems 2
1.7 Random Selection of Points from Intervals 7
Review Problems 9



2 Combinatorial Methods 13

2.2 Counting Principle 13
2.3 Permutations 16
2.4 Combinations 18
2.5 Stirling’ Formula 31
Review Problems 31



3 Conditional Probability and Independence 35

3.1 Conditional Probability 35
3.2 Law of Multiplication 39
3.3 Law of Total Probability 41
3.4 Bayes’ Formula 46
3.5 Independence 48
3.6 Applications of Probability to Genetics 56
Review Problems 59




4
Distribution Functions and
Discrete Random Variables
63

4.2 Distribution Functions 63
4.3 Discrete Random Variables 66
4.4 Expectations of Discrete Random Variables 71
4.5 Variances and Moments of Discrete Random Variables 77
4.6 Standardized Random Variables 83
Review Problems 83