Question

Suppose the following data were obtained from the admissions office of a 2-year junior college. Of the first-year class (F), 75% became sophomores (S) the next year and 25% dropped out (D). Of those who were sophomores during a particular year, 90% graduated (G) by the following year and 10% dropped out.

(a) [8 pts] Set up a Markov chain transition matrix with states D, F, G, and S that describes the scenario. Hint: Although not explicitly stated, you can assume that if someone started out as (D), dropped out, then they stay dropped out. Also, if they start out as (G), graduated, then they stay graduated.

(b) [5 pts] Which states are absorbing and why?

(c) [10 pts] Determine the fundamental matrix. You must show all the work for this, including the row operations to find the inverse matrix. You may check your answer with part d.

(d) [6 pts] In part c, you should have gotten T =1 .75

0 1. Use T to find the 01 expected number of years it would take a first-year student to graduate. You must show some work or explain how you used T; giving a single number as your answer will receive no credit.

(e) [8 pts] Determine the probability that an entering first-year student will eventually graduate. (Hint: you need to use S). Again, you must show work for this solution to receive credit.

Answer 1

NOTE: AS PER THE Q&A GUIDELINES I HAVE DONE 4 PARTS OF THE PROBLEM.

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