Multivariate Discrete Distributions

Abstract

We have provided a detailed overview of distributions of one discrete or one continuous random variable in the previous chapter. But often in applications, we are just naturally interested in two or more random variables simultaneously. We may be interested in them simultaneously because they provide information about each other, or because they arise simultaneously as part of the data in some scientific experiment. For instance, on a doctor’s visit, the physician may check someone’s blood pressure, pulse rate, blood cholesterol level, and blood sugar level, because together they give information about the general health of the patient. In such cases, it becomes essential to know how to operate with many random variables simultaneously. This is done by using joint distributions. Joint distributions naturally lead to considerations of marginal and conditional distributions. We study joint, marginal, and conditional distributions for discrete random variables in this chapter. The concepts of these various distributions for continuous random variables are not different; but the techniques are mathematically more sophisticated. The continuous case is treated in the next chapter.