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It would have been better if you would have worked through the problem one time to see what is involved but I will go ahead with the example.

This is the initial vector:

This is the transition matrix. Notice how all the rows sum to 1. This means the matrix is a stochastic matrix.

The answer is:

So after 5 years 60% of the population still lives in the city.

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Sorry for the delay, I am having an emergency here and will be busy. Sorry for the problem.

]]>I would just calculate it by hand and get the answer, but it is too long so let's pretend that I got it correctly.

]]>It wasn't actually a question I was posing. It is part of a lesson on Markov chains for anonimnystefy. But that is okay that you answered it, I will check your answer.

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https://docs.google.com/viewer?a=v&q=ca … CaQbkXgpfQ

Bottom paragraph.

]]>2)It's nice and useful.

3)Yes,but i have never understood it.

]]>**The city of Albany is experiencing a movement of its population. At present 85% of the population lives in the city and 15% in the suburbs. Each year 7% of the population moves to the suburbs and 1% of the suburb population move back to the city. Assuming the population of the city + the suburbs stays constant. After 5 years what percentage of people will live in the city?**

You can work on that problem on your own before I show you how to do it with a Markov chain.

A couple of questions:

1)Have you heard of the Feynmann story of why he was such a good problem solver?

2)What do you think of back engineering as a method of problem solving?

3)Have you seen gAr and my work on these Markov chains?

I have a long distance call coming in so I will be busy for a while.

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