### Discrete Random Variables

**mathStatica** automatically handles discrete random variables in the standard way. The only difference is that, when we define the density, we add a flag to tell *Mathematica* that the random variable is {Discrete}. To illustrate, let the discrete random variable have probability mass function (pmf)

, for .
Here, parameter is the probability of success, while parameter is a positive integer. In *Mathematica*, we enter this as:

This is known as the Pascal distribution. Here is a plot of :

**Fig. 1: ** The pmf of a Pascal discrete random variable

Here is the cdf, equal to :

The mean and variance of are given by:

The probability generating function (pgf) is :