1) Student transitions. Consider this model for a small, prestigious academy with a difficult curriculum. The academy has 4 grades for its students: entry level (g1), novice (g2), experienced (g3), and advanced (g4).Each year studentseither are demoted, stay in their grade, are promoted, orquit. In addition, many of the g4 studentsgraduate. Absorbing states are defined as quit or graduate. In particular,
From entry level (g1): 2% remain g1, 87% promoted to g2, 1% promoted to g3, and 10% quit
From novicelevel (g2): 3% demoted to g1, 4% remain g2, 78% promoted to g3, and 15% quit
From experienced level (g3): 7% demoted to g2, 5% remain g3, 68% promoted to g4, 14% quit, and 6% graduate early
From advanced level (g4): 8% demoted to g3, 11% remain g4, 25% quit, and 56% graduate
Hint ("H.W.xls")
a) Below are possible Markov transition matrices for the above scenario.
Choice 1:
|
Position
|
Grade 1
|
Grade 2
|
Grade 3
|
Grade 4
|
Quit
|
Graduate
|
|
Grade 1
|
0.02
|
0.87
|
0.01
|
|
0.1
|
|
|
Grade 2
|
0.03
|
0.04
|
0.78
|
|
0.15
|
|
|
Grade 3
|
|
0.07
|
0.05
|
0.68
|
0.14
|
0.06
|
|
Grade 4
|
|
|
0.08
|
0.11
|
0.25
|
0.56
|
|
Quit
|
|
|
|
|
1
|
|
|
Graduate
|
|
|
|
|
|
1
|
|
|
|
|
|
|
|
|
Choice 2:
|
Position
|
Grade 1
|
Grade 2
|
Grade 3
|
Grade 4
|
Quit
|
Graduate
|
|
Grade 1
|
0.02
|
0.77
|
0.11
|
|
0.1
|
|
|
Grade 2
|
0.03
|
0.04
|
0.78
|
|
0.15
|
|
|
Grade 3
|
|
0.07
|
0.05
|
0.68
|
0.14
|
0.06
|
|
Grade 4
|
|
|
0.08
|
0.11
|
0.25
|
0.56
|
|
Quit
|
|
|
|
|
1
|
|
|
Graduate
|
|
|
|
|
|
1
|
|
|
|
|
|
|
|
|
Select the most appropriate transition matrix that best represents this model as a Markov chain from the above choices and place a check next to the selection from the following possible answers. Place your answer on the answer sheet on the front cover as well.
1) ____________ Choice 1 is the most appropriate answer
2) ____________ Choice 2 is the most appropriate answer
3) ____________ Neither Choice 1 nor Choice 2 is the most appropriate answer
Attachment:- Assignment.rar