Suppose that, for 1 1, the probability density function of (Y1, Y2) is given by f (y1
Chapter 5, Problem 5.65(choose chapter or problem)
Suppose that, for 1 1, the probability density function of (Y1, Y2) is given by f (y1, y2) = [1 {(1 2ey1 )(1 2ey2 )}]ey1y2 , 0 y1, 0 y2, 0, elsewhere. a Show that the marginal distribution of Y1 is exponential with mean 1. b What is the marginal distribution of Y2? c Show that Y1 and Y2 are independent if and only if = 0. Notice that these results imply that there are infinitely many joint densities such that both marginals are exponential with mean 1.
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