Continuous N-Dimensional Random Variables

Abstract

This chapter extends the results of Chapters 10-13 for one and two continuous random variables to N continuous random variables. Our discussion will mirror Chapter 9 quite closely, the difference being the consideration of continuous rather than discrete random variables. Therefore, the descriptions will be brief and will serve mainly to extend the usual definitions for one and two jointly distributed cont inuous random variables to an N-dimensional random vector. One new concept that is introduced is the orthogonality principle approach to prediction of the outcome of a random variable based on the outcomes of several other random variables. This concept will be useful later when we discuss prediction of random processes in Chapter 18.