Distribution of Functions of Random Variables

This chapter focuses on the distributions of functions of random variables. It also focuses on the joint distribution functions of two or more discrete and continuous random variables. The chapter explores the concept of marginal and conditional probability distributions. It analyses the moment-generating functions of functions of two or more random variables. The chapter deals with linear functions of two or even more independent random variables. It describes the correlation between two random variables. The notions of the probability function of a pair of discrete random variables and the probability density function of a pair of continuous random variables extend without special difficulties to sets of three or more random variables. The moment-generating function has an important property that is if two random variables X and Y have the same moment-generating function, then their cumulative distribution functions are identical.