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

MATH152 April 2017

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Question A 20
Suppose $P$ 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 $P$.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Let $I_{0}={\begin{bmatrix}1\\0\\0\\0\\0\\0\\0\\0\end{bmatrix}}$ be the intial step (at stage $1$). After $13$ steps, we have $I_{13}=P^{13}I_{0}.$ Then the $7$th entry shows the probablity that it is in state $7$. The MATLAB script we should use should look something like I0 = zeros(8,1); I0(1) = 1; I13 = P^(13)*I0; I13(7)