The (cumulative) distribution function, or probability distribution function, F(x) is the mathematical equation that describes the probability that a variable X is less that or equal to x, i.e.
F(x) = P(X≤x) for all x
where P(X≤x) means the probability of the event X≤x.
A cumulative distribution function has the following properties:
1. F(x) is always non-decreasing, i.e. \frac{d}{dx} F(x)\geq 0
2. F(x) = 0 at x = -∞ or minimum
F(x) = 1 at x = ∞ or maximum
