Page 62 - DMTH404_STATISTICS

Statistics Sachin Kaushal, Lovely Professional University

Notes Unit 5: Functions of Random Variables

CONTENTS

Objectives
Introduction
5.1 Function of Two Random Variables
5.1.1 Direct Method

5.1.2 Transformation Approach
5.2 Functions of More than Two Random Variables
5.3 Summary
5.4 Keywords

5.5 Self Assessment
5.6 Review Questions
5.7 Further Readings

Objectives

After studying this unit, you will be able to:
 Discuss the functions of random variables
 Describe the transformation approach

Introduction

In the last unit, we have introduced bivariate distributions and multivariate distributions. Most
of the times we would like to know the probabilistic behaviour of a function g(X,Y) of the
random vector (X,Y). The function g could be either the sum X+Y or the max (X,Y) or some other
function depending on the phenomenon under study. We give two approaches for obtaining the
distribution function of a function of two random variables. These distributions can be considered
as distributions of functions of independent standard normal random variables. Properties of
these distributions are investigated in detail.
5.1 Function of Two Random Variables

We shall talk about functions of two random variables and discuss methods for obtaining their
distribution functions. Some of the important functions X which we shall consider are X + Y, XY,
X
, max (X,Y), |X-Y|.
Y

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