# Discrete Distribution

Just as a frequency distribution associates variable values to corresponding frequencies, a probability distribution associates the outcomes of a random experiment to corresponding probabilities.

### Discrete Probability Distribution Definition

An association of the outcomes of a discrete probability distribution with corresponding probabilities if the following two conditions are satisfied.

- The sum of all the probabilities in the sample space = 1; that is ∑P(X) = 1
- The probability of each event must be between 0 and 1. that is 0 ≤ P(X) ≤ 1.

The expectation of a discrete distribution E(X) = Mean μ = ∑X.P(X)

The variance of the discrete distribution X, σ

^{2}= [E(x)]

^{2}- μ

^{2}.

Let us look at some of the discrete distributions.