Hi! I need help on this problem:

Two teams play a series of games, stopping as soon as one of the teams has three wins. Assume the games are independent and that the chance the first team wins is an unknown parameter (0, 1). Let X denote the number of games the first team wins, and Y the number of games the other team wins.

a) Find the joint mass function of X and Y .

b) If our data are X and Y , find a minimal sufficient statistic.

c) Is the minimal sufficient statistic in part (b) complete? Explain your reasoning.