A coin has probability p of coming up heads and 1 - p of coming up tails, where p ∈ (0, 1). The first stage of an experiment consists of tossing this coin a known total of M times and recording X, the number of heads. In the second stage, the coin is tossed until a total of X + 1 tails have come up. The number Y of heads observed in the second stage along the way to getting the X + 1 tails is then recorded. This experiment is repeated independently a total of n times and the two counts (X_i, Y_i) for the ith experiment are recorded, i = 1, ..., n. Obtain a statistic that is minimal sufficient for p and derive its distribution.