test1 - Math 370 Actuarial Problemsolving Spring 2008 A.J...

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Unformatted text preview: Math 370, Actuarial Problemsolving Spring 2008 A.J. Hildebrand Practice Test, 1/28/2008 About this test. This is a diagnostic test made up of a random collection of 20 problems from past Course 1/P actuarial exams. It is intended for students who have already taken of Math 408 or equivalent (e.g., Math 461), to give them an idea of where they stand. It also helps me identify areas that should be emphasized in this course. This test will not count, so if you do poorly, it won’t affect your grade. If you want, you can take the test anonymously—just leave out your name on the answer sheet. However, in order for the test to provide meaningful feedback, I’d like everyone who is taking the test to turn in an answer sheet. Note for those currently enrolled in 408: If you have not already taken 408, it does not make much sense to take this test, since most of the problems are on material not yet covered in 408. Instead work the set-theory practice problems. Rules. This test is intended to simulate the real thing as closely as possible, so you should abide by the same rules. In particular, no notes, books, etc., and use calculators only for basic arithmetic operations. In particular, do not use calculators to compute integrals, derivatives, or to plot graphs. In the actuarial exam you are limited to calculators without such functions. It goes without saying that you shouldn’t cheat. Don’t copy an answer from your neighbor; if you do so, you are only cheating yourself, and you are defeating the purpose of this course. Time. You have 2:00 hours for this exam. This works out to 6 minutes per problem, which is the same as what you get in an actuarial exam. Use the time wisely, and don’t let yourself get bogged down in a lengthy calculation. If you don’t get a problem at first, move on to the next one. Answers/solutions. I will post an answer key and partial solutions on the course webpage, www.math.uiuc.edu/ ∼ hildebr/370 . 1 Math 370 A.J. Hildebrand Spring 2008 1. An actuary studying the insurance preferences of automobile owners makes the fol- lowing conclusions: (i) An automobile owner is twice as likely to purchase collision coverage as disability coverage. (ii) The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage. (iii) The probability that an automobile owner purchases both collision and disability coverages is 0 . 15. What is the probability that an automobile owner purchases neither collision nor disability coverage? (A) 0 . 18 (B) 0 . 33 (C) 0 . 48 (D) 0 . 67 (E) 0 . 82 2 Math 370 Practice Test, 1/28/2008 Spring 2008 2. A device runs until either of two components fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is f ( x,y ) = 1 27 ( x + y ) for 0 < x < 3 and 0 < y < 3, otherwise....
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test1 - Math 370 Actuarial Problemsolving Spring 2008 A.J...

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