Conditional Probability Density Functions

Abstract

A discussion of conditional probability mass functions (PMFs) was given in Chapter 8. The motivation was that many problems are stated in a conditional format so that the solution must naturally accommodate this conditional structure. In addition, the use of conditioning is useful for simplifying probability calculations when two random variables are statistically dependent. In this chapter we formulate the analogous approach for probability density functions (PDFs). A potential stumbling block is that the usual conditioning event X = x has probability zero for acontinuous random variable. As a result the conditional PMF cannot be extended in a straightforward manner. We will see, however, that using care, a conditional PDF can be defined and will prove to be useful.