Page 56 - DMTH404_STATISTICS

Statistics Sachin Kaushal, Lovely Professional University

Notes Unit 4: Random Variable

CONTENTS

Objectives
Introduction
4.1 Definition of a Random Variable
4.2 Probability Distribution of a Random Variable

4.2.1 Discrete and Continuous Probability Distributions
4.2.2 Cumulative Probability Function or Distribution Function
4.3 Summary
4.4 Keywords

4.5 Self Assessment
4.6 Review Questions
4.7 Further Readings

Objectives

After studying this unit, you will be able to:
 Define random variables
 Define probability distributions of random variable

Introduction

In order to discuss the applications of probability to practical situations, it is necessary to
associate some numerical characteristics with each possible outcome of the random experiment.
This numerical characteristic is termed as random variable.
4.1 Definition of a Random Variable

A random variable X is a real valued function of the elements of sample space S, i.e., different
values of the random variable are obtained by associating a real number with each element of
the sample space. A random variable is also known as a stochastic or chance variable.
Mathematically, we can write X = F(e), where e ÎS and X is a real number. We can note here that
the domain of this function is the set S and the range is a set or subset of real numbers.

Example 1: Three coins are tossed simultaneously. Write down the sample space of the
random experiment. What are the possible values of the random variable X, if it denotes the
number of heads obtained?

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