In: Math
In a tennis match, the first serve percentage is a key statistic. Having an accurate (and fast) first serve is seen as an important advantage to winning a match. Let theta be the probability of getting the first serve in on any point in a tennis game. For each of the four situations below, give a prior distribution for theta, explaining each in a sentence. You may assume the winner is determined from the best of three sets, (so the first player to win two sets will win).
(a) The point is the first point of the match.
(b) It is the beginning of the second set and the server has won the first set.
(c) It is the beginning of the second set and the server has lost the first set.
(d) If the server wins the next point, they will win the match.