Probability, Statistics and Random Processes

3

Mathematical Expectation

Prerequisites

Before you start reading this unit, you should:

• Be able to differentiate between discrete and continuous random variables
• Be familiar with pmf and pdf
• Calculate marginal density of random variables

Learning Objectives

After going through this unit, you would be able to

• Understand the expectation, variance, conditional mean, Chebychev’s theorem, moments, moment generating function, and characteristic function
• Calculate expectation, variance, conditional mean, given joint density functions of X and Y
• Apply Chebychev’s theorem to a random variable with some mean and variance

INTRODUCTION

Consider for instance, a salesman’s average monthly income. This average may not be equal to any of his monthly pay. ...