Distribution function

Question 1

Definition distribution function

Answer 1

Let X be a real valued random variable (not necessarily discrete). We define its distribution function, denoted by Fx, as follows

Fx: R–>[0,1]

Fx = P(X<x)

Question 2

General properties of the distribution function

Answer 2

1) Fx is increasing
2) Fx is right continuous
3) lim Fx(x) = 0 lim Fx(x) = 1
x->-∞ x->+∞
4) ∆Fx(x) = P(X=x)