Stuart Klugman <stuart.klugman@drake.edu> on 11/05/98 04:50:02 PM
Please respond to Stuart Klugman <stuart.klugman@drake.edu>
To: Study group 4B <studygroup4B@lists.casact.org>
cc: (bcc: Colleen Walker/AmericanRe)
Subject: 4B Questions 1-10
I have just received a copy of the exam and worked through 1-10. Here are
some comments.
(1) For 1-9 I get A,B,A,E,A,E,C,C,D
(2) Two different approaches have been suggested for number 8. Both are
correct. The condidtional variance formula works. Also, raw moments, but
not variances can be obtained as weighted averages. So it is easy to get
the first and second moment and use them to get the variance.
(3) Number 7 has been questioned. Assuming the most powerful test is to
be used, the rejection region is X>c. That can be proved by the
Neyman-Pearson lemma, or by just reasoning that small alpha means large
observations. The p-value is then Pr(X>c|alpha=.5) = (10,000/9,610,000)^.5
= .032. And so reject for a 0.05 significance level and accept for a 0.02
level.
(4) For number 10 I get none of the above! The 50 type Y's below the
limit contribute f(y). The 75 type Y's above the limit each contribute
1-F(k). The 75 type Z's above the deductible each contribute
f(z)/[1-F(k)]. Thus we have the numerator from answers B and D, but the
denominator from answer E. COMMENTS?
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Stuart Klugman, FSA
Principal Financial Group Professor of Actuarial Science
Drake University
2507 University Avenue
Des Moines, IA 50311 USA
ph: 515-271-4097
e-mail: Stuart.Klugman@drake.edu