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232a1.w08

# 232a1.w08 - k = 0 1 2 9(a Compute Pr K x = 0 Pr K x = 1 Pr...

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ACTSC 232 – WINTER 2008 ASSIGNMENT 1 DUE: FRIDAY FEB 1 (hand in to the instructor in class) 1. The function 18000 - 110 x - x 2 18000 has been proposed for the survival function for a mortality model. (a) What is the implied limiting age ω ? (b) Verify that the function satisﬁes the conditions for the survival function S T 0 ( x ). (c) Calculate 20 p 0 . (d) Calculate the survival function for a life age 20. (e) Calculate the probability that a life aged 20 will die between ages 30 and 40. (f) Calculate the force of mortality at age 50. [12 marks] 2. Show that R ω - x 0 t p x μ x + t dt = 1. [6 marks] 3. You are given that q x + k = 0 . 1( k + 1),
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Unformatted text preview: k = 0 , 1 , 2 ,..., 9. (a) Compute Pr[ K x = 0], Pr[ K x = 1], Pr[ K x = 2] and Pr[ K x ≥ 3]. (b) Let Y = min( K x , 3), where K x is the curtate future lifetime random variable. i. Calculate E( Y ). ii. Calculate Var( Y ). [10 marks] 4. (a) Show that when μ x = Bc x , we have t p x = g c x ( c t-1) , where g is a constant that you should identify. (b) For a mortality table constructed using the above force of mortality, you are given that 10 p 50 = 0 . 861716 and 20 p 50 = 0 . 718743; calculate the values of B and c . [12 marks] 1...
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