CDF

Another basic one today as I want to spend more time working problems than writing.

A Cumulative Distribution Functions (cdf), F(x) for a random variable X is defined as F(x) = P(X ≤ x). From this definition and the basic axioms, we get a few noteworthy properties:

1. F(x) is a monotonically increasing function of x (using National Institute of Standards and Technology definition which allows the function to be flat in spots; some authors would call this non-decreasing).
2. lim_{x→ -∞} F(x) = 0 and lim_x→∞ F(x) = 1
3. F(x) is right-continuous, that is for all x₀, lim_x↓x0 F(x) = F(x₀)