Distribution Function (C.D.F.) of a continuous random
is defined as
is the probability density function of X.
From the above definition it follows (from the Fundamental Theorem of Calculus) that
It should be noted
that the C.D.F. of a continuous random variable is therefore a continuous
function (ie. its graph has no "jumps"). Also
it possesses similar properties to the C.D.F. of a discrete random
variable (click on the Note button below for full details).