probability question

Q3 (a) Let X be a nonnegative integer valued random variable with probability mass function px(k). Derive an expression for P(X is odd) in terms of its probability generating function Px (2) defined on some domain C C R.(b) Let X = Pn(X) and Y = Nb(r,p) be two independent random variables. Let W = X +Y. (i) Write down the probability generating function for W, Pw(2).(ii) Which values of the parameters A, r, and p will ensure that W is more likely to take on even values than odd values? Justify your answer.{iii} In terms of}... r, and p, evaluate pw} = P[W = 1} in two different ways: one using the probability generating function: and the other using the convolution formula