Multivariate Discrete Distributions

Abstract

We have provided a detailed treatment of distributions of one discrete or one continuous random variable in the previous chapters. 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. Or, in agri cultural studies, one may want to study the effect of the amount of rainfall and the temperature on the yield of a crop and therefore study all three random variables simultaneously. At other times, several independent measurements of the same object may be available as part of an experiment and we may want to combine the various measurements into a single index or function. In all 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 considera tions of marginal and conditional distributions. We will study joint, marginal, and conditional distributions for discrete random variables in this chapter. The concepts of joint, marginal, and conditional distributions for continuous random variables are not different, but the techniques are mathematically more sophisticated. The continuous case will be treated in the next chapter.