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RelativeResourceManagere2

# RelativeResourceManagere2 - MATH 471 Actuarial Theory I...

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MATH 471: Actuarial Theory I Midterm #2 November 11, 2009 There are 7 problems on this midterm for a total of 60 points. Put your name and lecture section time on the cover of the exam booklet. Make sure that all your work is shown in the exam booklet. It is possible to earn partial credit by showing all your work. Keep at least five decimal places during each of your calculations. Refer to the accompanying tables when necessary. Good luck! 1. For a continuous whole life annuity of 1 per year on (x): (i) δ t = 0.05 for 0 < t 15, δ t = 0.06 for 15 < t (ii) μ x ( t ) = 0.02 for 0 < t 15, μ x ( t ) = 0.04 for 15 < t Calculate the single benefit premium. (8 points) 2. Let Z be the present value random variable for a whole life insurance on (x) with a benefit of 10,000 payable at the moment of death. Assume μ x ( t ) = 0.03 and δ t = 0.06 for t 0. (a) Determine the cumulative distribution function of Z . (5 points) (b) Calculate the 65th percentile of the distribution of Z . (4 points) 3. Suppose Z is the present value random variable for a 2-year pure endow- ment insurance of 1 on (x). You are given:

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RelativeResourceManagere2 - MATH 471 Actuarial Theory I...

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