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Problem 3. Professor Ding and 10 students play the following game. For every time t = 1, 2, . . ., each of them tosses a pcoin (a pcoin produces a head with probability p in every toss) and they stop right after Professor Ding has obtained a head for the rst time (for instance, if Professor Ding gets a head in his 3rd toss, then everyone has tossed 3 times). Let N be the number of times Professor Ding 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 VarM