Problem 3. A mathematician is perpetually in one of four possible states: 0 = wo

Question

Problem 3. A mathematician is perpetually in one of four possible states: 0 = working without a problem; 1 working but feeling a little sluggish; 2 working but just barely; 3- disfunctional. The mathematician changes states according to somewhat random processes (generous students bringing coffee, the Keurig breaking, etc.) via the following transition matrix: 0.8 0 0 0.9 14 .6 0 0 04 3 .65 0 02 .1 .35 .1 Verify that this is a regular Markov chain (i.e., find a value of r) and find a steady-state distribution, along with a 1-sentence description of what this vector represents). You can do this by hand or by computer.

Explanation / Answer

Since all the values in the matrix is positive and also A^2 is also positive. Wes can say that regular Markov chain is there.

The vector represents the regular markov chain the markov chain.

Since by the definition of regular, there is a k such that any two vertices are joined by a path of length k, it follows that pk has all positive elements.

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