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Probability, Statistics and Random Processes by Pappu Kousalya

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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. ...

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