Multiple Random Variables

In many experiments an observation is expressible, not as a single numerical quantity, but as a family of several separate numerical quantities. To be able to describe such experiments mathematically we must study the multidimensional random variables. This chapter introduces the basic notations involved and study joint, marginal, and conditional distributions. The joint distribution of a multiple random variables uniquely determines the marginal distributions of the component random variables, but, in general, knowledge of marginal distributions is not enough to determine the joint distribution. It examines independent random variables and investigates some consequences of independence. The chapter then deals with functions of several random variables and their induced distributions, and considers moments, covariance, and correlation. Finally, the chapter focuses on conditional expectation and ordered observations.