**Introduction:**

The probability distribution often deals with variables as a ‘quantity that may assume any one of a set of values’. In probability distribution we deal with random variables - variables whose observed value is determined by chance.

**Random Variable:**

The random variable in probability distribution that represent outcomes of an experiment if these outcomes are numerical or if real numbers can be assigned to them.

**Types of Random variables:**

1. Discrete Random variable

2. Continuous Random variable.

**Definition:**

If a Discrete random variable in probability distribution takes only a finite or a countable number of values, it is called a discrete random
variable.** **

** Example :**

1. The number of heads obtained when two coins are tossed is a discrete random variable as X assumes the values 0, 1 or 2 which form a countable set.

2. Number of Aces when ten cards are drawn from a well shuffled pack of 52 cards.

The random variable X assumes 0, 1, 2, 3 or 4 which is again a countable set.

i.e., X (No aces) = 0, X (one ace) = 1, X (two aces) = 2,

*X* (three aces) = 3, X (four aces) = 4** **

**Definition:**

A Continuous Random Variable in probabiltiy distribution *X* is said to be
continuous if it can take all possible values between certain given limits. i.e., *X* is said to be continuous
if its values cannot be put in 1 − 1 correspondence with *N*, the set of Natural numbers.

**Examples:**

1. The life length in hours of a certain light bulb.

2. Let *X* denote the *ph* value of any chemical compound which is randomly selected between 0 and 14 is possible.

3. If in the study of ecology of a lake, *X* = the depth at such location is a
continuous random variable. The limit will be between the maximum and minimum depth in the region sampled.