Let p be the probability of your textbook author Bruce making a free throw shot.

(a) Consider the prior ¼

¡

p

¢

Æ beta(1,1). (Beta with ® Æ 1 and ¯ Æ 1.) Write and sketch the prior density.

Does this prior seem to you to be a good choice for representing uncertainty about p?

(b) Bruce attempts one free throw shot and misses. Write the likelihood and posterior densities. Find the posterior mean b pBayes and the MLE b pmle.

(c) Bruce attempts a second free throw shot and misses. Find the posterior density and mean given the two shots. Find theMLE.

(d) Bruce attempts a third free throw shot and makes the basket. Find the estimators b pBayes and b pmle.

(e) Compare the sequence of estimators. In this context is the Bayes orMLE more sensible?