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347.2009.final.comments - Section 5.11 is important Problem...

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Comments on Final Exam, Spring 2009 Problem 3 You cannot use geometry calculations to find probabilities unless the density function is constant on the support. Problem 4a A few people after calculating the value of F ( y ) on the support of Y , the interval [0,1], said that F ( y ) = 0 elsewhere.” This is impossible – the cdf is a non-decreasing function. The correct statement is that F ( y ) = 0 for y < 0 and F ( y ) = 1 for y > 1. The density function, f ( y ), is “0 elsewhere,” but not the distribution function, F ( y ). Problems 3 and 4 I think it would be useful to get more practice doing similar problems. Problem 7 This problem is very much like Example 5.32 on page 286 of the text, which was done in class (slides 11-13 of Section 5.11), and homework problems 5.135 and 5.138 on page 289. It uses the Double Expectation Theorem. In the Exam P Sample Questions on the SOA site, they added a question this year which uses the Double Expectation Theorem for Variances, so I would assume that they feel that the material in
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Unformatted text preview: Section 5.11 is important. Problem 9 • The performance on this problem was better than on the similar problem on the Make-Up. Once again, I want to emphasize that determining the kind of distribution being described is a crucial first step in solving “word” problems involving random variables. Extra Credit Problem 10 • This is the kind of problem I might use if I were writing Exam P. A few of the people who did part (a) were sloppy in how they wrote things, and came out with the complementary probability. Since the probability was ଵ ଶ , the complementary probability is also ଵ ଶ , so the numeric answer was correct, but the method was not. If I were writing Exam P (or rewriting the final), I would make sure the correct answer was not ଵ ଶ and put the complementary probability as one of the choices....
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