4. Data for the progression of college students at a particular college are summarized in the following matrix of transition probabilities: Graduate Drop Out Freshman Sophomore Junior Senior 0.00 0.00 Graduate 1.00 0.00 0.00 0.00 0.00 0.00 0.65 0.10 0.00 0.00 0.00 0.00 0.00 Drop Out 1.00 0.00 0.20 0.15 Freshman 0.00 0.15 0.00 0.00 Sophomore Junior 0.00 0.00 0.75 0.05 0.85 0.00 0.90 0.10 0.00 Senior 0.05 0.00 0.00 0.05 a. What states are absorbing states? b. Interpret the transition probabilities for a sophomore. c. Compute the probabilities that a sophomore will graduate and that a sophomore will drop out. d. In an address to the incoming class of 600 freshmen, the dean asks the students to look around the auditorium and realize that about 50% of the freshmen present today will not make it to graduation day. Does your Markov process analysis support the dean's statement? Explain. e. Currently, the college has 600 freshmen, 520 sophomores, 460 juniors, and 420 seniors. What percentage of the 2000 students attending the college will eventually graduate?

4. Data for the progression of college students at a particular college are summarized in the following matrix of transition probabilities: Graduate Drop Out Freshman Sophomore Junior Senior 0.00 0.00 Graduate 1.00 0.00 0.00 0.00 0.00 0.00 0.65 0.10 0.00 0.00 0.00 0.00 0.00 Drop Out 1.00 0.00 0.20 0.15 Freshman 0.00 0.15 0.00 0.00 Sophomore Junior 0.00 0.00 0.75 0.05 0.85 0.00 0.90 0.10 0.00 Senior 0.05 0.00 0.00 0.05 a. What states are absorbing states? b. Interpret the transition probabilities for a sophomore. c. Compute the probabilities that a sophomore will graduate and that a sophomore will drop out. d. In an address to the incoming class of 600 freshmen, the dean asks the students to look around the auditorium and realize that about 50% of the freshmen present today will not make it to graduation day. Does your Markov process analysis support the dean's statement? Explain. e. Currently, the college has 600 freshmen, 520 sophomores, 460 juniors, and 420 seniors. What percentage of the 2000 students attending the college will eventually graduate?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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