the register of a law school has compiled the following statistics on the progre

Question

the register of a law school has compiled the following statistics on the progress of the school's students working toward the LLB degree: of the first-year students in a particular year, 85% successfully complete their course of studies and move on to the second year, where as 15 % drop out of the program; of the second-year students in a particular year, 92 % go on to the third year, where as 8% drop out of the program; of the third-year students in a particular year, 98% go on to graduate at the end of year, where as 2% drop out of the program. a) Construct the transition matrix associated with the Markov process. b) Find the steady-state matrix. c) Determine the probability that a beginning law student enrolled in the program will go on to graduate.

Explanation / Answer

c)Probability=0.76636

Year1 Year2 Year3 0.85 0.92 0.98 State Probability 0 1       2           3 P(success) 1 0.85 0.85*0.92=0.782    0.782*0.98=0.76636 0 0.15 1-0.7820=0.218    1-0.76636=0.23364 matrix ( 1   0)(0.85 0.15) P1 P1*(0.92    0.08) P2 P2*(0.98   0.02) P3

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