In Exercise 5.65, we considered random variables Y1 and Y2 that, for 1 1, have joint

Chapter 5, Problem 5.85

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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 and established that the marginal distributions of Y1 and Y2 are both exponential with mean 1. Find a E(Y1) and E(Y2). b V(Y1) and V(Y2).c E(Y1 Y2). d E(Y1Y2). e V(Y1 Y2). Within what limits would you expect Y1 Y2 to fall?

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