Let N ~ Poi(4) and X; are independent. Define Bin(2, 3), for i = 1, 2, ... The random variables N, X1, X2, ... = N = = X

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Let N Poi 4 And X Are Independent Define Bin 2 3 For I 1 2 The Random Variables N X1 X2 N X 1 (74.13 KiB) Viewed 42 times

Let N ~ Poi(4) and X; are independent. Define Bin(2, 3), for i = 1, 2, ... The random variables N, X1, X2, ... = N = = Xi, where Y = 0) if N = 0. = i=1 = = (a) Show that Gy(z) = E(zY) = exp (32 + 22 – 3), ZER. [3 marks] (b) Determine P(Y = 0) and P(Y = 1). [2 marks] (c) Determine EY and Var(Y). [2 marks] (d) Let Vị and V, be two independent random variables with Vi ~ Poi(;), i = 1, 2. Show that there exists 11, 12 > 0 such that V1 + 2V2 has the same distribution [3 marks] as Y.