Suppose you participate in a chess tournament in which you play n games. Since you are a very average player, each game is equally likely to be a win, a loss, or a tie. You collect 2 points for each win, 1 point for each tie, and 0 points for each loss. The outcome of each game is independent of the outcome of every other game. Let X_i be the number of points you earn for game i and let Y equal the total number of points earned over the n games.

(a) Find the moment generating functions φ_Xi(s) and φ_Y (s).

(b) Find E[Y] and Var[Y].