The number of attempts, y, required for a certain basketball player to make a 25 foot shot, is observed, in order to choose one of the following two hypotheses:
h1 (outstanding player) : y has the geometric distribution with parameter p = 0.5.
h0 (average player) : y has the geometric distribution with parameter p = 0.2.
(a) describe the ml decision rule. express it as directly in terms of y as possible.
(b) find pfalse alarm and pmiss for the ml rule.
(c) describe the map decision rule under the assumption that h0 is a priori twice as likely as h1. express the rule as directly in terms of y as possible.
(d) find the average error probability, pe, for both the ml rule and the map rule, using the same prior distri- bution given in part (c). for which rule is the average error probability smaller?