Discrete and Continuous random variables

Discrete and Continuous random variables

Random variables are generally classified into two types, based on the values they take such as Discrete random variable and Continuous random variable.

Discrete random variable

A random variable is said to be discrete if it takes only a finite or countable infinite number of values.

Example 9.4

Consider the experiment of tossing a coin

If X (Head) =1, X (Tail) = 0

Then X takes the values either 0 or 1

This is a discrete random variable.

Example 9.5

Consider the experiment of tossing a coin till head appears.

Let random variable X denote the number of trials needed to get a head. The values taken by it will be 1, 2, 3, ..

It is discrete random variable taking countable infinite values.

Continuous random variable:

A random variable X is said to be continuous, if it takes values in an interval or union of disjoint intervals. (A rigorous definition is beyond the scope of the book).

Example 9.6

If X is defined as the height of students in a school ranging between 120 cms and 180 cms, Then the random variable X is {x/120 cms < x < 180 cms } is a continuous random variable.

Example 9.7

Let the maximum life of electric bulbs is 1500 hrs. Life time of the electric bulb is the continuous random variables and it is written as X = {x/0 ≤ x ≤ 1500}