Summary: Definition. (See p.70) Suppose (S, A, P) is a probability space and X is a random variable. We define
FX : R - R
by setting
FX (x) = P(X x) for x R.
We call FX the cumulative distribution function (cdf) of X.
Note that
x1 x2 = FX (x1) FX(x2);
lim
x-
FX(x) = 0;
lim
x
FX(x) = 1
and that
lim
xa
FX(x) = FX(a) for a R.
We say X is discrete (see p.59) if there is countable set C such that P(X c) = 0 in which case we
define
pX : R R

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics