# A1 - (c) i n l x + t μ x + t dt = l x-l x + n 3....

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ACTSC 232 - Spring 2010 - Assignment 1 Due: Friday, May 28 at 11:30 am 1. The function 20900 - 80 x - x 2 20900 has been proposed for the survival function S 0 ( x ) for a mortality model. (a) What is the implied limiting age ω ? (b) Verify that S 0 ( x ) satis±es the 3 conditions for a survival function. (c) What is the pdf of the future lifetime random variable for a life age 0? (d) Calculate 20 p 0 . (e) Calculate 10 | 5 q 0 . (f) Calculate the mean future lifetime for a life age 0. (g) Calculate the median future lifetime for a life age 0. (h) Determine the survival function for a life age 20. (i) What is the pdf of the future lifetime random variable for a life age 20? (j) Calculate the probability that a life age 20 will die between ages 30 and 40. (k) What is the mean age at death of a life age 20. (l) Calculate the force of mortality at age 50. 2. Show that: (a) d dx t p x = t p x ( μ x - μ x + t ) (b) i ω - x 0 t p x μ x + t dt = 1
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Unformatted text preview: (c) i n l x + t μ x + t dt = l x-l x + n 3. Makeham’s mortality law (similar to Gompertz) assumes that μ x = A + Bc x for all x ≥ 0. (a) Show that t p x = s t g c x ( c t-1) , and specify the values of s and g . (b) Suppose you know the values of 5 p 45 , 5 p 50 , and 5 p 55 . Show that c = ( log ( 5 p 55 )-log ( 5 p 50 ) log ( 5 p 50 )-log ( 5 p 45 ) ) . 2 (c) With A = 0 . 0035, B = 0 . 0001, and c = 1 . 07, calculate 4 . 5 | 6 . 3 q 48 . 6 . 4. Given the following life table, x 52 53 54 55 56 57 58 l x 89,948 89,089 88,176 87,208 86,181 85,093 82,719 Calculate the probability that (a) a life age 52 lives to age 58 (b) a life age 52 dies between age 54 and 56 (c) a life age 55 dies before age 57 (d) BONUS a life age 52.3 dies between age 55 and 55.5, assuming UDD. 1...
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## This note was uploaded on 03/20/2011 for the course ACTSC 232 taught by Professor Matthewtill during the Summer '08 term at Waterloo.

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