Exam due on Nov 18, Wednesday 9:30-11:00 EST

Mathematical
Statistics and
Data Analysis

3 Joint Distributions 71

1. 3.1 Introduction 71
2. 3.2 Discrete Random Variables 72
3. 3.3 Continuous Random Variables 75
4. 3.4 Independent Random Variables 84
5. 3.5 Conditional Distributions 87
   1. 3.5.1 The Discrete Case 87
   2. 3.5.2 The Continuous Case 88
6. 3.6 Functions of Jointly Distributed Random Variables 96
   1. 3.6.1 Sums and Quotients 96
   2. 3.6.2 The General Case 99
7. 3.7 Extrema and Order Statistics 104
8. 3.8 Problems 107

4 Expected Values 116

1. 4.1 The Expected Value of a Random Variable 116
   1. 4.1.1 Expectations of Functions of Random Variables 121
   2. 4.1.2 Expectations of Linear Combinations of Random Variables 124
2. 4.2 Variance and Standard Deviation 130

4.2.1 A Model for Measurement Error 135

1. 4.3 Covariance and Correlation 138
2. 4.4 Conditional Expectation and Prediction 147

4.4.1 Definitions and Examples 147

4.4.2 Prediction 152

1. 4.5 The Moment-Generating Function 155
2. 4.6 Approximate Methods 161
3. 4.7 Problems 166