A bag is filled with two types of coins. One type of coin has probability of heads p0. A second type of coin has probability of heads p1. A fraction π0 of the coins have probability of heads p0. A fraction π1= 1−π0 of the coins have probability of heads p. A coin is randomly chosen and flipped untilk heads appear. The number of fliped takes to get k heads is Y. Required:
Find the best decision rule for deciding which coin was chosen to minimize the probability of making an error in the decision.