Random Variable

A set of numerical values assigned to all possible outcomes of a random experiment are called random variables. The random variable can be briefly written as r.v. If we write A, B,…, F on the six faces of a die, these letters are not an r.v. If we write some numerical values on the six faces of a die like I, 2, 3,…, 6, we have a set of values called r.v. Suppose we select two bulbs from a certain lot having good and defective bulbs. Let G stand for good and D stand for defective. There are four possible outcomes which are GG, GD, DG and DD. Each outcome can be assigned a numerical value. Let us count the number of defective bulbs in each outcome. We can write:

 Outcome No. of Defective Bulbs GG 0 GD 1 DG 1 DD 2

Thus the numerical values 0, 1, 2 are the values of the random variable where the random variable is the number of defective bulbs in this discussion. A random variable is denoted by a capital letter $X$. Here $X$ is the number of defective bulbs. The small letters ${x_1},{x_2}, \ldots ,{x_n}$ are used for the specific values of the random variable. A random variable is also called a chance variable. If we have two or more random variables we can use the letters $X,Y,Z$ for them. A random variable may be discrete or continuous.