Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 03 (d)
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Question B 03 (d) 

A random walk problem with two states has a transition matrix d) After many time steps what state is the walker more likely to be? Justify briefly. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

In your result from c) let the number of step sizes n go to infinity. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Using our answer from c), we can study the limit where goes to infinity. In this case the probability vector approaches Hence, it is more likely, that the walker will be be in state 2 after a large number of steps, since the 2nd entry in the vector is larger than the first entry. 