# What is a cumumlative distribution function?

Shows the distribution of probabilities under graph.

Integrating over a range gives us the probability within that range.

Let X be a random variable, discrete / continuous.

F(x) is the cumulative distribution function of the random variable X.

F(x) = Pr(X <= x)

## Case 1: X is discrete

F(x) = sumof f(t), for ranges t<=x. = sumof Pr(X = t), for range t <= x.

It is a step function.