Let the unknown probability that a basketball player makes a shot successfully be θ. Suppose your prior on θ is uniform and that she makes two shots in a row. Assume that the outcomes of the two shots are independent. (a) What is the posterior density of θ? (b) What is the Bayes estimator under squared error loss for θ? (c) What is the Bayes estimator under absolute error loss for θ? (d) Consider the impact of
Let the unknown probability that a basketball player makes a shot successfully be θ. Suppose your prior on θ is uniform and that she makes two shots in a row. Assume that the outcomes of the two shots are independent. (a) What is the posterior density of θ? (b) What is the Bayes estimator under squared error loss for θ? (c) What is the Bayes estimator under absolute error loss for θ? (d) Consider the impact of
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Let the unknown probability that a basketball player makes a shot successfully be θ. Suppose your prior on θ is uniform and that she makes two shots in a row. Assume that the outcomes of the two shots are independent. (a) What is the posterior density of θ? (b) What is the Bayes estimator under squared error loss for θ? (c) What is the Bayes estimator under absolute error loss for θ? (d) Consider the impact of the prior choice θ ∼ Beta(1, 1). How would your answer in (b) change if you instead used Beta(0.1, 0.1)? Beta(10,10)?
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