Solved: In Exercise 5.65, we considered random variables Y1 and Y2 that, for 1 1, have
Chapter 5, Problem 5.101(choose chapter or problem)
In Exercise 5.65, we considered random variables Y1 and Y2 that, for 1 1, have joint density function given by f (y1, y2) = [1 {(1 2ey1 )(1 2ey2 )}]ey1y2 , 0 y1, 0 y2, 0 elsewhere. We established that the marginal distributions of Y1 and Y2 are both exponential with mean 1 and showed that Y1 and Y2 are independent if and only if = 0. In Exercise 5.85, we derived E(Y1Y2). a Derive Cov(Y1, Y2). b Show that Cov(Y1, Y2) = 0 if and only if = 0. c Argue that Y1 and Y2 are independent if and only if = 0.
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