Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP, 2nd Edition

Chapter 6Distribution of Functions of Random Variables

The focus of this chapter is on the distributions of functions of random variables.

Topics Covered

• Joint distributions of two discrete random variables
• Joint distributions of two continuous random variables
• Mean value and variance of functions of two random variables
• Conditional distributions
• Correlation between two random variables
• Joint distributions of several random variables
• Moment‐generating functions of two or more random variables

Learning Outcomes

After studying this chapter, the reader will be able to

• Understand the concept of discrete and continuous distributions of functions of two or more random variables and use them to solve real‐world problems.
• Understand the concept of marginal and conditional probability distributions.
• Determine the moment‐generating functions of functions of two or more random variables.

6.1 Introduction

In Chapters 4 and 5, we discussed various phenomena by enlisting a (single) random variable and studying its distribution and characteristics. However, in many situations, experiments are performed that involve two or more random variables. For example, we may be interested in the diameter and length of rods, the number of dots on two dice when rolled simultaneously, say , where , or the composition of a Monel (70% nickel, 30% copper) alloy, where we may focus on solid contents, ...