Let X and Y be discrete random variables, where Y follows the Poisson distribution with parameter lembda. Given Y, assume X follows Bin(Y, p) where p belongs to (0; 1) is a constant. Answer the following questions. (i) Compute EX. (ii) Compute Var(X) by using the formula: Var(X) = E[Var(X|Y )] + Var(E(X|Y )): (iii) Derive the probability mass function of X. %3D

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