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A2 Let X ~ Geo(p) with p E (0, 1). Conditionally on X, Y takes the value X with probability 1/2 and the value 3X

A2 Let X ~ Geo(p) with p E (0, 1). Conditionally on X, Y takes the value X with probability 1/2 and the value 3X with probability 1/2. (a) Compute Eyx [Y[X]. [2] (b) Compute E[ Y]. (c) Compute Varyix (Y|X). (d) Show that Var(Y) = 6p-2 -5p-1

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