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Math 472 Spring 2011 Midterm 2 Formulas

# Math 472 Spring 2011 Midterm 2 Formulas - MATH 472/567...

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MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Midterm #2 Additional Problems: Spring 2011 1. For a triple decrement model on (50): (i) μ (1) 50 ( t ) = 1 50 - t for 0 t < 50 (ii) μ (2) 50 ( t ) = 2 50 - t for 0 t < 50 (iii) μ (3) 50 ( t ) = 3 50 - t for 0 t < 50 (a) Calculate the probability that (50) decrements due to cause 2. (1/3) (b) Calculate the probability that (50) decrements due to cause 2 during the fifth year. (1/40) 2. Complete the following double decrement table, assuming l ( τ ) 40 = 100,000: x q (1) x q (2) x p ( τ ) x l ( τ ) x d (1) x d (2) x 40 0.01 0.03 41 0.02 0.04 42 0.03 0.05 43 0.04 0.06 3. Using the Illustrative Service Table, calculate: (a) 6 p ( τ ) 56 (0.6859) (b) 6 q ( w ) 56 (0.0238) (c) 5 | q ( i ) 56 (0) 1

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4. For students entering a college, you are given the following from a double decrement model: (i) 1000 students enter the college at t = 0. (ii) Students leave the college due to either failure or voluntary exit. (iii) The probability of an entering student staying in college for one year is 0.80. (iv) The probability of an entering student staying in college for two years is 0.70. (v) The probability of a first-year student failing during the year is twice the probability of a second-year student failing during the year. (vi) The probability of an entering student voluntarily exiting in the second year is 0.09.
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