# 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.