Math 472 HW 4 Solutions

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

This preview shows pages 1–2. Sign up to view the full content.

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:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/18/2011 for the course MATH 472 taught by Professor Zhu during the Spring '08 term at University of Illinois, Urbana Champaign.

### Page1 / 7

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online