Tutorial_1_Solutions

Tutorial_1_Solutions - Name: userid: ACTSC 232 – Winter...

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Unformatted text preview: Name: userid: ACTSC 232 – Winter 2011 Tutorial #1 – Jan 10, 2011 1. Consider a proposed survival function S ( t ) = 1 10 √ 100- t, ≤ t ≤ 100. (a) Verify that this is indeed a valid survival function. (That is, verify that it meets the three necessary conditions discussed in class.) Answer: i. S (0) = 1 10 √ 100- 0 = 1 10 · 10 = 1 . ii. S (100) = 1 10 √ 100- 100 = 0, so all lives die by age 100. iii. d dt S ( t ) = d dt 1 10 √ 100- t = 1 10 · (- 1 2 ) (100- t )- 1 / 2 ≤ ∀ t ∈ [0 , 100] . Thus all of the required conditions are met. (b) Find the probability that a newborn dies between the ages of 10 and 20. Answer: S (10)- S (20) = 1 10 √ 100- 10- 1 10 √ 100- 20 = 0 . 949- . 894 = 0 . 054 . (c) Find the probability that a 30-year old lives to at least age 60. Answer: Here we must find the probability that a newborn lives to age 60, conditioned on the fact that they lived to at least age 30....
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This note was uploaded on 01/27/2011 for the course ACTSC 232 taught by Professor Matthewtill during the Winter '08 term at Waterloo.

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Tutorial_1_Solutions - Name: userid: ACTSC 232 – Winter...

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