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Unformatted text preview: MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #9: Spring 2011 Assigned April 6, due April 13 1. I argued in lecture that: k | q xy 6 = ( k p xy )( q x + k : y + k ). Starting with the Law of Addition for pmfs, show that with independent lives (x) and (y): k | q xy = ( k q y )( k p x )( q x + k ) + ( k q x )( k p y )( q y + k ) + ( k p x )( k p y )( q x + k )( q y + k ), and interpret this result using words. 2. Suppose both (40) and (60) have independent future lifetimes and mortality that is subject to de Moivres Law with = 100. Calculate: (a) e 40:60 . (34.44) (b) var [ T (40 : 60)]. (113.58) (c) cov [ T (40 : 60) , T ( 40 : 60)]. (64.20) 3. A fully discrete life insurance on two independent lives, ages 25 and 35, pays 1000 at the end of the year of the first death and 2000 at the end of the year of the second death. Furthermore: (i) Level benefit premiums are payable at the beginning of the year while both are alive....
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