Science:Math Exam Resources/Courses/MATH152/April 2017/Question A 20
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Question A 20 

Suppose was the transition matrix for a random walk with 8 states that had been entered into MATLAB. What commands would you use to compute the probability that if the system started in state 1, it would be in state 7 after 13 time steps? 
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 

Recall the definition of the transition matrix . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let be the intial step (at stage ). After steps, we have Then the th entry shows the probablity that it is in state . The MATLAB script we should use should look something like I0 = zeros(8,1); I0(1) = 1; I13 = P^(13)*I0; I13(7) 