An individual can contract a particular disease with probability 0.17. A sick person will recover dur- ing any particular time period with probability 0.44 (in which case they will be considered healthy at the beginning of the next time period). Assume that people do not develop resistance, so that pre- vious sickness does not influence the chances of contracting the disease again. Model as a Markov chain, give transition matrix on your paper. Find the probability that a healthy individual will be sick after two time periods.

An individual can contract a particular disease with probability 0.17. A sick person will recover dur- ing any particular time period with probability 0.44 (in which case they will be considered healthy at the beginning of the next time period). Assume that people do not develop resistance, so that pre- vious sickness does not influence the chances of contracting the disease again. Model as a Markov chain, give transition matrix on your paper. Find the probability that a healthy individual will be sick after two time periods.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let us consider the population of people living in a city and its suburb and the migration within this population from the city and the suburbs to the city and the suburbs. The migration of these populations from and to each other is given by a stochastic matrix [.95 .03] P = |.05 .97 The entries in this matrix were obtained from collected data that demonstrates individuals are 95 % likely to remain in the city, 5 % likely to move from the city to the suburbs, 3 % likely to move from the suburbs to the city, and 97 % likely to remain in the suburbs. Now suppose in the year 2000 60 % or .6 percent of people live in the city and 40 % or .4 percent of people live in the suburbs. What will be the percentage of people living in the city be in the year 2001? What will be the percentage of people living in the suburbs be in 2002? Hint: Recall, for a general Markov Chain (S, ro, P) the initial vector ro is required to merely be a probability vector, that is, a vector whose entries add up to 1.…
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