## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Discrete probability distribution

A discrete probability distribution shall be understood as a probability distribution characterized by a probability mass function. Thus, the distribution of a random variable X is discrete, and X is then called a discrete random variable, if

$sum_u Pr(X=u) = 1$

as u runs through the set of all possible values of X. It follows that such a random variable can assume only a finite or countably infinite number of values. For the number of potential values to be countably infinite even though their probabilities sum to 1 requires that the probabilities decline to zero fast enough: for example, if $Pr(X=n) = frac{1}{2^n}$ for n = 1, 2, ..., we have the sum of probabilities 1/2 + 1/4 + 1/8 + ... = 1.

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