# hw1-12 - (iii) There is an 8% chance of a 70-year old...

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MATH 471: Actuarial Theory I Homework #1: Fall 2010 Assigned August 25, due September 1 1. If F ( x ) = x 110 for 0 x 110 (de Moivre’s Law), ﬁnd expressions for the following; where 0 x 110 for (a) – (b), and 0 t 70 for (c) – (e): (a) f ( x ) (b) s ( x ) (c) t p 40 (d) t q 40 (e) the p.d.f. of T(40) 2. Suppose: s ( x ) = 10 , 000 - x 2 10 , 000 for 0 x 100. Calculate: q 49 . (0.013) 3. Let s ( x ) = ( 100 100+ x ) 2 for x 0. Calculate: (a) The probability that (25) will survive at least 40 more years. (0.5739) (b) The probability that (30) will die within the next 20 years. (0.2489) (c) The probability that (35) will die between ages 45 and 60. (0.1549) 4. Show: t p x = t + u q x - t q x + t + u p x . 5. You are given the following information: (i) The probability that two 70-year olds are both alive in 20 years is 0.16. (ii) The probability that two 80-year olds are both alive in 20 years is 0.01.

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Unformatted text preview: (iii) There is an 8% chance of a 70-year old surviving the next 30 years. (iv) All lives are independent and have the same expected mortality. Calculate the probability that an 80-year old will survive to age 90. (0.5) ————THERE ARE MORE PROBLEMS ON THE BACK ———— 1 6. You are given: t | q = 0.10 for t = 0, 1, . .., 9. Calculate: 2 p 5 . (0.6) 7. Suppose mortality follows modiﬁed (or generalized) de Moivre’s Law , where: s ( x ) = ( ω-x ω ) α for 0 ≤ x ≤ ω , α > 0. Note that regular de Moivre’s Law is a special case of this modiﬁed law with α = 1. Show: t p x = ( ω-x-t ω-x ) α for 0 ≤ t ≤ ( ω-x ), α > 0. 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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hw1-12 - (iii) There is an 8% chance of a 70-year old...

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