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Richa Nandra, Lovely Professional University Unit 9: Variance of a Random Variable and their Properties

Unit 9: Variance of a Random Variable Notes

and their Properties

CONTENTS
Objectives
Introduction

9.1 Mean and Variance of a Random Variable
9.1.1 Moments
9.2 Summary
9.3 Keywords
9.4 Self Assessment

9.5 Review Questions
9.6 Further Readings

Objectives

After studying this unit, you will be able to:
 Discuss variance of random variable
 Describe the properties random variable

Introduction

In last unit you will studied about expected random variable. This unit will provide you variance
of a random variable.

9.1 Mean and Variance of a Random Variable

The mean and variance of a random variable can be computed in a manner similar to the
computation of mean and variance of the variable of a frequency distribution.
Mean

If X is a discrete random variable which can take values X , X , ..... X , with respective probabilities
1 2 n
as p(X ), p(X ), ...... p(X ), then its mean, also known as the Mathematical Expectation or Expected
1 2 n
Value of X, is given by:
n
E(X) = X p(X ) + X p(X ) + ...... + X p(X )   X p(X ) .
1 1 2 2 n n i i
i 1

The mean of a random variable or its probability distribution is often denoted by , i.e.,
E(X) = .

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