A 1 [17 marks] Let X N Poi(n), where (0,1). Let the conditional distribution of Y given X = k be given by Y|X = k ~ N(k, 1) for all k = NU {0}. (a) Compute E[Y]. [3] (b) Compute Var(Y). [4] (c) Compute the mgf My (s). [7] (d) [Type] Explain how the expected value and the variance of Y could be computed starting from the mgf obtained in part c above. Note that you should not actually carry out these calculations: you should instead describe which calculations are needed in words rather than through formulae. [3]