Let the joint pdf of X and Y be given byf(x, y) = 121 2 expx2 2xy + y22(1 2),where

Chapter 3, Problem 5

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Let the joint pdf of X and Y be given byf(x, y) = 121 2 expx2 2xy + y22(1 2),where || < 1. Show that the marginal pdfs arefX(x) = 12ex2/2,fY (y) = 12ey2/2.The random variables X and Y are said to have a two-dimensional (or bivariate)normal pdf. Also note that X and Y are not independent unless = 0.

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