Let X and Y be independent binomial random variables with parameters (m, p) and (n, p), respectively. Let W = X + Y. (a) Derive the probability mass function of W directly from the joint proba- bility mass function of X and Y. (b) More generally, if X and Y are independent random variables with pa- rameters (m, px ) and (n, py ), respectively, find the MGF of W = X + Y. Is its distribution bimomial? (c) What is the distribution of 3X? Is it binomial