Page 6 - Probability, Random Variables and Random Processes

Contents

Chapter 1. Probability 1

1.1 Introduction 1
1.2 Sample Space and Events 1
1.3 Algebra of Sets 2
1.4 The Notion and Axioms of Probability 5
1.5 Equally Likely Events 7
1.6 Conditional Probability 7
1.7 Total Probability 8
1.8 Independent Events 8
Solved Problems 9

Chapter 2. Random Variables 38

2.1 Introduction 38
2.2 Random Variables 38
2.3 Distribution Functions 39
2.4 Discrete Random Variables and Probability Mass Functions 41
2.5 Continuous Random Variables and Probability Density Functions 41
2.6 Mean and Variance 42
2.7 Some Special Distributions 43
2.8 Conditional Distributions 48
Solved Problems 48

Chapter 3. Multiple Random Variables 79

3.1 Introduction 79
3.2 Bivariate Random Variables 79
3.3 Joint Distribution Functions 80
3.4 Discrete Random Variables - Joint Probability Mass Functions 81
3.5 Continuous Random Variables - Joint Probability Density Functions 82
3.6 Conditional Distributions 83
3.7 Covariance and Correlation Coefficient 84
3.8 Conditional Means and Conditional Variances 85
3.9 N-Variate Random Variables 86
3.10 Special Distributions 88
Solved Problems 89

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