consider an unfair coin tossed at random independently where probability of getting head is 2 3 . (a) (geometric) suppose that y is the number of tails until you get the first head. find the moment generating function (m.g.f.) of y , and compute the mean of the number of tails until the first head. (b) generalize the result in (a) by considering a coin with probability of getting head p. what is the m.g.f and mean?