Cumulative Distribution Function (CDF)

Cumulative Distribution Function (CDF)

For a random variable X, there is a cumulative distribution function for X:

P (X \leq x) = F (x) (- \infty < x < \infty)

This function has 2 features:

F(x) is monotonous and not decreasing:

F (x_{1}) \leq F (x_{2})

for

x_{1} \leq x_{2}

when x → + $\infty$ , F(x) → 1; when x → - $\infty$ , F(x) → 0

CDF is defined for both Random Variables & Probability distributions#Discrete variables and Random Variables & Probability distributions#Continuous variables.