X1 x2 x3 ... xn are n independent identically distributed, Ask an Expert

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X1, X2, X3, ... Xn are n independent, identically distributed random variables with expectation of 5 and variance of 4 (E[Xi] = 5, Var (Xi) = 4) and n is large. Now if random variable Y is defined as Y = (X1 + X2 + X3 + ... +Xn)/n

(a) Determine E[Y]?
(b) Determine Var(Y)?
(c) Without the knowledge of pdf of Xi, do we know pdf of Y.

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