# 4 ans - assumed to be uniformly distributed between integer...

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MATH 471: Actuarial Theory I Homework #4: Fall 2010 Assigned September 15, due September 22 1. Fill in the missing entries of the following life table: x l x p x q x d x e x 96 10 97 7 98 3 99 1 1 2. You are given the following life table: x l x p x d x 50 800 0.97 51 33 52 31 53 29 54 0.96 Calculate the expected number of deaths between ages 53 and 55. (56.32) 3. You are given the following life table: x l x d x p x 0 1000.0 0.875 1 125.0 2 3 0.680 4 182.5 5 200.0 Calculate 2 | q 0 . (0.1875) ————THERE ARE MORE PROBLEMS ON THE BACK ———— 1

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4. If q 70 = 0.04 and q 71 = 0.05, calculate the probability that (70.6) will die within the next 0.5 years under: (a) the UDD assumption within each year of age. (0.02131) (b) the constant force assumption within each year of age. (0.02123) (c) the Balducci assumption within each year of age. (0.02115) 5. Assume a uniform distribution of deaths between integer ages. Show: l x + t = (1 - t )( l x ) + t ( l x +1 ), where x is an integer and 0 t 1. 6. Suppose mortality follows the Illustrative Life Table, where deaths are

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Unformatted text preview: assumed to be uniformly distributed between integer ages. Calculate the median future lifetime for (40). (37.58) 7. Mr. Ucci has only 3 hairs left on his head and he will not be growing any more. Also: (i) The future mortality of each hair follows: k | q x = 0.1( k + 1) where k = 0, 1, 2, 3 and x is Mr. Ucci’s age. (ii) Hair loss follows the hyperbolic assumption at fractional ages. (iii) The future lifetimes of the 3 hairs are independent. Calculate the probability that Mr. Ucci is bald (has no hair left) by age (x + 2.5). (0.1183) 8. For a 4-year college, you are given the following probabilities for dropout from all causes: q = 0.15, q 1 = 0.10, q 2 = 0.05, q 3 = 0.01 Dropouts are uniformly distributed over each year. Calculate the temporary 1.5-year complete expected college lifetime of a student entering the second year. (1.39) 2...
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## This note was uploaded on 02/02/2011 for the course MATH 471 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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4 ans - assumed to be uniformly distributed between integer...

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