Answers to 2005 Final Exam
Answers to multiple choice questions: (c), (a), (d), (c), (a), (c), (b), (b), (b), (d).
11. See pp. 71-72 of the notes.
12. We have
P(M1|y) = 1
2·m1(y)
m(y),
where
m(y) = 1
2m1(y) + 1
4m2(y) + 1
4m3(y)
and
mi(y) = ZΘ
fi(y|θ)πi(θ)dθ, i = 1,2,3.
13. See pp. 73-74 of the notes.
14. See pp. 1, 34-35 of the notes.
15. A manufacturing plant produces parts on a daily basis. The “true” proportion of defective
parts changes from day to day. On a given day the number of defective parts in a sample of
parts has a binomial distribution with proportion θi. We might assume that θ1, . . . , θnover
a period of ndays are i.i.d. beta random variables. See pp. 327-328 of the notes for more on
hierarchical models.
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