Suppose that the random variables Y1 and Y2 have joint probability density function, f

Chapter 5, Problem 5.32

(choose chapter or problem)

Suppose that the random variables Y1 and Y2 have joint probability density function, f (y1, y2), given by (see Exercise 5.14) f (y1, y2) = 6y2 1 y2, 0 y1 y2, y1 + y2 2, 0, elsewhere. a Show that the marginal density of Y1 is a beta density with = 3 and = 2. b Derive the marginal density of Y2. c Derive the conditional density of Y2 given Y1 = y1. d Find P(Y2 < 1.1|Y1 = .60).

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