Page 140 - DMTH404_STATISTICS

Statistics Richa Nandra, Lovely Professional University

Notes Unit 10: Approximate Expressions for

Expectations and Variance

CONTENTS
Objectives

Introduction
10.1 Theorems on Expectation
10.1.1 Theorems on Variance
10.2 Joint Probability Distribution
10.2.1 Marginal Probability Distribution

10.2.2 Conditional Probability Distribution
10.2.3 Expectation of the Sum or Product of two Random Variables
10.2.4 Expectation of a Function of Random Variables

10.6 Summary
10.7 Keywords
10.8 Self Assessment
10.9 Review Questions
10.10 Further Readings

Objectives

After studying this unit, you will be able to:
 Discuss theorem on expectation

 Explain joint probability distribution
Introduction

In last unit you have studied about variance of random variable. This unit will explain you joint
probability distribution.

10.1 Theorems on Expectation

Theorem 1.
Expected value of a constant is the constant itself, i.e., E(b) = b, where b is a constant.
Proof.
The given situation can be regarded as a probability distribution in which the random variable
takes a value b with probability 1 and takes some other real value, say a, with probability 0.
Thus, we can write E(b) = b × 1 + a × 0 = b

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