Mr. Stat and 10 students play the following game. For every time t = 1, 2, . . ., each of them tosses a p-coin (a p-coin produces a head with probability p in every toss) and they stop right after Mr. Stat has obtained a head for the first time (for instance, if Mr. Stat gets a head in his 3rd toss, then everyone has tossed 3 times). Let N be the number of times Mr. Stat has tossed at the end of the game, and let M be the total number of heads obtained by all these 11 players at the end of the game.

(a) Find the conditional distribution for N given M = 1.

(b) Compute Var(M).