Random Variable

A set of numerical values assigned to the all possible outcomes of the random experiment are called random variable. 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 a 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 some numerical value. Let us count number of defective bulbs in each outcome. We can write

No. of Defective Bulbs


Thus the numerical values 0, 1, 2 are the values of the random variable where 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 chance variable. If we have two or more than two random variables we can use the letters X,Y,Z for them. A random variable may be discrete or continuous.