Discrete Distributions

When an outcome is discrete (numerical) or qualitative, data collected by an experiment is referred as categorical. We conventionally denote random variables by uppercase letters X, Y, Z, from the end of the alphabet. Particularly if the random variable X takes numerical values such as 1,2,3, (or 0,1,2,3,), we call it a discrete random variable. The statement such as “X = 2” is an event, and therefore, is associated to the probability . We can assign for all the possible values j = 1,2,3, (or j = 0,1,2,3,), which will completely describe the "probabilistic nature" of X, that is, the probability distribution of X. P(X=j) is often called a frequency function, and simply written by f(j).