Coins I and II have probabilities p1 and p2 of head, respectively. One of these two coins is chosen at random and tossed till the first tail occurs. Let X denote the number of tosses required.
(a) Determine the PMF of the random variable X
(b) Determine a sufficient condition on p1 and p2 that makes a geometric random variable. In that case, what's the parameter of the geometric distribution for X.