Question: Let T R be the set {(x, y): 0 x 1, 0 y }and let X and Y be random variables with joint probability

Let T R be the set {(x, y): 0 x 1, 0

Let T R be the set {(x, y): 0 x 1, 0 y }and let X and Y be random variables with joint probability density function fx,y(x, y) = (6x (1 - x)exy, (x, y) = T otherwise a) Show that the marginal distribution of X is Be(2; 2), and that the conditional probability density function of Y given X = x (for 0 x 1) isEx (X). b) Hence use conditional expectation to find E(Y) (12 marks) (8 marks)

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