The Cumulative Distribution Function (C.D.F.) of a continuous random variable X is defined as

where f 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).