Math 472 HW 4 Solutions - MATH 472/567: Actuarial Theory...

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MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #4: Spring 2011 Assigned February 9, due February 23 1. Consider a double decrement model with: (i) μ (1) 60 ( t ) = 1 30 - t for 0 t < 30. (ii) μ (2) 60 ( t ) = 1 20 - t for 0 t < 20. Determine: (a) The joint “pdf” of T (60) and J (60). (b) The probability that (60) decrements due to cause 1. (1/3) (c) The probability that (60) decrements due to cause 1 in the third or fourth year from now. (17/300) 2. Paul, age 33, is an actuarial science professor. His career is subject to two decrements: (i) Decrement 1 is mortality: μ (1) 33 ( t ) = t 50 for t 0. (ii) Decrement 2 is leaving academic employment: μ (2) 33 ( t ) = t 40 for t 0. (a) Calculate the probability that Paul remains an actuarial science professor for less than five years. (0.4302) (b) Determine: f T | J ( t | 2). (c) Given: R 0 t 2 exp[ - at 2 ] dt = π 4 a 1 . 5 for a > 0, calculate: E [ T | J = 2]. (5.91) 3. Complete the following triple decrement table:
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Math 472 HW 4 Solutions - MATH 472/567: Actuarial Theory...

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