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canon14
03-16-2010, 01:08 PM
I just need my work verified for the problem below. Any help/guidance is much appreciated.

A faculty member can be either an assistant professor, an associate professor, or a full professor. In terms of departmental standing, a full professor is above an associate professor, who is in turn, above assistant professor. At the end of each academic year, 13% of assistant professors become associate professors and 18% leave the department; 21% of associate professors become full professors, and 17% leave the department; and 9% of full professors leave the department. Demotion never occurs. It is also known that 60% of faculty members enter the department as an assistant professor, 30% as an associate professor, and 10% as a full professor. When an assistant professor leaves the department, 60% of time is on “bad terms” and 40% of the time is on “good terms”. When a full professor leaves the department, 90% of the time is on “good terms”.

a. What is the probability that a faculty member leaves the department on “bad terms”?
b. Given that a faculty member enters the department as an associate professor, how long would you expect him to stay in the department?

This is what I have for part A:

Assume 100 Professors
Assistant = 60
Associate = 30
Full = 10

End of the year
13% Assistant --> Associate = 60*.13 = 7.8
21 % Associate --> Full = 30*.21 = 6.3

Leave
18% Assistant = 60*.18 = 10.8
17% Associate = 30*.17 = 5.1
9% Full = 10*.09 = 0.9

Total Leave = 10.8 + 5.1 + 0.9 = 15.5


Assistant (60% Bad) = 4.32 (Leave Good); 6.48(Leave Bad)
Associate (25% Bad) = 0.95 (Leave Good); 2.85 (Leave Bad)
Full (10% Bad) = 0.09 (Leave Good); 0.81 (Leave Bad)

Total Leave Bad = 6.48 + 2.85 + 0.81 = 10.14

Probability of faculty leaving bad = 10.14/15.5 = 65.4%