Math 472 HW 11 Solutions

# Math 472 HW 11 Solutions - MATH 472/567 Actuarial Theory...

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MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #11: Spring 2011 Assigned April 20, due April 27 1. The number of coins Lucky Tom ﬁnds in successive blocks as he walks to work follows a homogeneous Markov model: (i) States 0, 1, 2 correspond to 0, 1, or 2 coins found in a block. (ii) The transition matrix is: Q = 0 . 2 0 . 5 0 . 3 0 . 1 0 . 6 0 . 3 0 . 1 0 . 5 0 . 4 (iii) Tom found zero coins in the ﬁrst block today. Calculate the probability that Tom will ﬁnd at least three coins in the next two blocks today. (0.42) 2. Barry is a world class sprinter. As time passes, it becomes more and more likely that he will drop from being a world class sprinter (State 0) to a decent sprinter (State 1). However, it is possible that with lots of training and hard work, one can move from being a decent sprinter back to a world class sprinter. Assuming a two-state Markov Chain with transitions at the end of the period; for t = 1, 2, . .., 10, the transition matrix is:

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## 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.

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Math 472 HW 11 Solutions - MATH 472/567 Actuarial Theory...

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