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In a tennis match, the first serve percentage is a key statistic. Having an accurate (and...

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Basic Math

In a tennis match, the first serve percentage is a keystatistic. Having an accurate (and fast) first serve is seen as animportant advantage to winning a match. Let theta be theprobability of getting the first serve in on any point in a tennisgame. For each of the four situations below, give a priordistribution for theta, explaining each in a sentence. You mayassume the winner is determined from the best of three sets, (sothe 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 wonthe first set.

(c) It is the beginning of the second set and the server haslost the first set.

(d) If the server wins the next point, they will win thematch.

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