. . Probability Mass Function The probability that a discrete random variable X takes on a particular value x , that is P X is frequently denoted by f x ( ) or p x ( ) . The function f x ( ) is typically called the probability mass function, although some authors also refer to it as the probability function or the frequency function.
In this chapter, when the random variable is discrete, the common terminology the probability mass function is used and its common abbreviation is pmf. Definition . (Probability mass function) If X is a discrete random variable with discrete values x x x x n then the function denoted by f (.) or p (.) and defined by k k k ), , , , for is called the probability mass function of X Theorem . (Without proof) The function f x ( ) is a probability mass function if and only if it satisfies the following properties for the set of real values x , x , x , ...
x n ... . (i) f x k ) ³ for k = , , , and (ii) f x k k ) =