TABLE OF CONTENTS In order to be able to handle the events in a sample space mathematically, it is useful to attach a numerical value to each elementary event. (Recall that elementary events are events that contain just one point.) The set of numerical values of the elementary events is called a random variable, usually abbreviated as r.v. Conventionally, random variables are represented by capital letters, e.g. X.
When the elementary events are themselves numbers, there is a natural way of doing this. But it is sometimes useful to attach numbers to qualitative events. For example, suppose the sample space considered is that of the sex of an occupant and consists of two possible outcomes, namely { male, female}.We could assign to the event male the number 0 and to the event female the number 1. The advantage of doing this is, for example, that if we consider n occupants and attach to occupant i the random variable X i, then the number of females among the n occupants can be represented as X 1 + X 2 + + X n (or equivalently by ? X i).
In this work we shall consider two types of random variables: discrete and continuous.
A random variable is said to be discrete if its range is a discrete (finite or countable) set of real numbers. Usually, the values are {0, 1, 2,
