No jacobian factors such as those in section 472

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Unformatted text preview: variables The previous two sections present examples with one random variable that is a function of two other random variables. For example, X + Y is a function of (X, Y ). In this section we consider the case that there are two random variables, W and Z, that are both functions of (X, Y ), and we see how to determine the joint pdf of W and Z from the joint pdf of X and Y. For example, (X, Y ) could represent a random point in the plane in the usual rectangular coordinates, and we may be interested in determining the joint distribution of the polar coordinates of the same point. 4.7. JOINT PDFS OF FUNCTIONS OF RANDOM VARIABLES 4.7.1 145 Transformation of pdfs under a linear mapping To get started, first consider the case that W and Z are both linear functions of X and Y. It is much simpler to work with matrix notation, and following the usual convention, we represent points in the plane as column vectors. So sometimes we write X instead of (X, Y ), and we write fX,Y ( u ) Y v instead o...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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