. . Cumulative Distribution Function from Probability Mass function Both the probability mass function and the cumulative distribution function of a discrete random variable X contain all the probabilistic information of X . The probability distribution of X is determined by either of them.
In fact, the distribution function F of a discrete random variable X can be expressed in terms of the probability mass function f ( x ) of X and vice versa. Example . If the probability mass function f x ( ) of a random variable X is find (i) its cumulative distribution function, hence find (ii) P X ≤ and, (iii) P X ≥ (i) By definition the cumulative distribution function for discrete random variable is F x x i i - - Probability Distributions < = for −∞< . F ( ) = P X i i