RelativeResourceManager12 - MATH 471 Actuarial Theory I...

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MATH 471: Actuarial Theory I Homework #12: Fall 2009 Assigned December 2, due December 9 1. Suppose the weather is modeled by a homogeneous Markov chain, with two possible states each day (no rain, rain), as follows: (i) The probability that it rains on a day is 0.50 if it rained on the prior day. (ii) The probability that it rains on a day is 0.20 if it did not rain on the prior day. (iii) Transitions between states can only occur at the end of the day. (a) Calculate the probability that it will be raining two days from now, given rain today. (0.35) (b) Calculate the probability that it will be raining each day for the next two days, given rain today. (0.25) 2. An actuarial student can change both titles and salaries each year. The titles and salaries (paid in a lump sum at the beginning of each year) are as follows: (i) Actuarial Student (State 0), $40,000 (ii) Actuarial Analyst (State 1), $60,000 (iii) Associate Actuary (State 2), $80,000 All transitions take place at the end of the year. The transition matrix for
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