Cumulative Distribution Function for Discrete Distribution

Theorem

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.

Then the cumulative distribution function of $X$ is given by:

$\map F x = \ds \sum_{x_i \mathop \le x} \map \Pr {X = x_i}$

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): distribution function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): distribution function