. . Cumulative Distribution Function or Distribution Function There are many situations to compute the probability that the observed value of a random variable X will be less than or equal to some real number x . Writing F x for every real number x , we call F x ( ) , the cumulative distribution function or distribution function of the random variable X and its common abbreviation is cdf .
Definition . : (cumulative distribution function) The cumulative distribution function F x ( ) of a discrete random variable X , taking the values x , such that x < with probability mass function f x i is F x i i