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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?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 1.00 Drop Out Freshman Sophomore Junior Senior 0.00 0.65 0.10 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.75 0.00 0.10 0.00 0.05 0.85 0.90 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?
Transcribed Image Text: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 1.00 Drop Out Freshman Sophomore Junior Senior 0.00 0.65 0.10 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.75 0.00 0.10 0.00 0.05 0.85 0.90 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?
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