Jim must make five years’ worth of progress to complete his doctorate degree at ABC University. However, he enjoys the life of a student and is in no hurry to finish his degree. In any academic year there is a 50% chance he may take the year off and a 50% chance of his pursuing the degree full time. After completing three academic years, there is a 30% chance that Jim may “bailout” and simply get a master’s degree, a 20% chance of his taking the next year off but continuing in the Ph.D. program, and 50% chance of his attending school full time toward his doctorate.

a. Express Jim’s situation as a Markov chain.

b. Determine the expected number of academic years before Jim’s student life comes to an end.
c. Determine the probability that Jim will end his academic journey with only a master’s degree.
d. If Jim’s fellowship pays an annual stipend of $15,000 (but only when he attends school), how much will he be paid before ending up with a degree?
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