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PDF of a continuous RV that is exponentially distributed with parameter α > 0:

Discrete Random Variables

If the CDF F_X(x) of a RV X is constant between any two consecutive values in a discrete set of increasing values of x, X is referred to as a discrete random variable.

Example

CDF of a discrete RV:

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Probability Mass Function

If a RV X is discrete, and F_X(x), has step increases at the points {..., x_-1, x₀, x₁, ...}, then:

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If there is a smallest value x_j at which a step increase occurs in F_X(x), then:

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p_i^X is referred to as the probability mass function (PMF) of X. {..., x_-1, x₀, x₁, ...} is referred to as the support of X. Note that p_i^X atx = x_i is often referred to as p_X(x_i).

The following are properties of a PMF:

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