In: Statistics and Probability
A large corporation collected data on the reasons both middle
managers and senior managers leave the...
A large corporation collected data on the reasons both middle
managers and senior managers leave the company. Some managers
eventually retire, but others leave the company prior to retirement
for personal reasons, including more attractive positions with
other firms. Assume that the following matrix of one-year
transition probabilities applies with the four states of the Markov
process being retirement, leaves prior to retirement for personal
reasons, stays as a middle manager, and stays as a senior
manager.
|
|
Leaves- |
Middle |
Senior |
|
Retirement |
Personal |
Manager |
Manager |
Retirement |
1.00 |
0.00 |
0.00 |
0.00 |
Leaves-Personal |
0.00 |
1.00 |
0.00 |
0.00 |
Middle Manager |
0.02 |
0.08 |
0.80 |
0.10 |
Senior Manager |
0.08 |
0.02 |
0.04 |
0.86 |
- What states are considered absorbing states? (retirement and
leaves personal, leaves personal and middle manager, middle manager
and senior manager, only retirement, only senior, or only leaves
personal)
Why?
- Interpret the transition probabilities for the middle
managers.
Probability of retirement =
Probability of leaving (personal) =
Probability of staying middle manager =
Probability of promotion to senior manager =
- Interpret the transition probabilities for the senior
managers.
Probability of retirement =
Probability of leaving (personal) =
Probability of staying middle manager =
Probability of promotion to senior manager =
- What percentage of the current middle managers will eventually
retire from the company? What percentage will leave the company for
personal reasons? If required, round your answers to one decimal
place.
Retire from the company = %
Leave the company for personal reasons = %
- The company currently has 940 managers: 670 middle managers and
270 senior managers. How many of these managers will eventually
retire from the company? How many will leave the company for
personal reasons? If required, round your answers to one decimal
place.
Retire from the company = %
Leave the company for personal reasons = %