Two friends Bob and Carol decide to play 5 sets of tennis. Before they begin pla

Question

Two friends Bob and Carol decide to play 5 sets of tennis. Before they begin playing, Carol and Bob agree to a wager: hell pay her $40 dollars if she wins and shell pay him $60 if he wins (shes a better tennis player). Carol wins two of the first three sets. Assume that the prior distribution on the probability p that Carol will win any particular set is a Beta distribution with alpha = 1.2 and beta = 0.8, and that the outcomes of the 5 sets are independent. Find the Bayes estimate for p given that Carol won 2 of the first 3 sets.

Explanation / Answer

Solution:

Carol won 2 of the first 3 sets. Carol wins any particular set with probability 'p' which has a prior of Beta( = 1.2, = 0.8)
After first 3 sets, no. of sets n = 3 & carol won y = 2.
E(p|y) is an estimation of the parameter 'p'.
so, p = E(p|y) = +y/+n+
putting n = 3 & y = 2 we get, p = 1.2 + 2/1.2+3+0.8 = 0.64

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