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. 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)

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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Question

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
Graduate
1.00
0.00
0.00
0.00
0.00
0.00
0.00
Drop Out
Freshman
0.00
1.00
0.00
0.00
0.00
0.00
0.20
0.15
0.65
0.00
0.00
0.00
0.90
0.00
0.00
0.85
0.00
0.10
Sophomore
Junior
0.15
0.75
0.10
0.00
0.00
0.05
Senior
0.05
0.00
0.00
0.00
0.05

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