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(a) It is given that a random variable X such that P(X =−1) =P(X = 1)...

(a) It is given that a random variable X such that P(X =−1) =P(X = 1) = 1/4, P(X = 0) = 1/2. Find the mgf of X, mX(t)

(b) Let X1 and X2 be two iid random varibles such that P(Xi =1)=P(Xi =−1)=1/2, i=1,2. Use the mgfs to prove that X and Y =(X1+X2)/2 have the same distribution

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