Matrix question: Suppose centuries ago, a group of people lived in an isolated small village. They loved their land and had no incentives to move. Assume that for the job opportunities, anyone living...

Matrix question:

Suppose centuries ago, a group of people lived in an isolated small village. They loved their land and had no incentives to move. Assume that for the job opportunities, anyone living in that village had five options, to become either afarmer, butcher, baker, teacher, ordoctor. For simplification, we name the above 5 job types as OptionA, B, C, D and E, respectively.

It is also known that:

1. Once a resident became a farmer, the probabilities for him/her to continue being a farmer or become a butcher, baker, teacher or doctor would be 50%, 28%, 10%, 10% and 2%, respectively.


2. Once a resident became a butcher, the probabilities for him/her to continue being butcher or become a farmer, baker, teacher or doctor would be 50%, 20%, 10%, 19% and 1%, respectively.


3. Once a resident became a baker, the probabilities for him/her to continue being a baker or become a farmer, butcher, teacher or doctor would be 50%, 20%, 20%, 8% and 2%, respectively.


4. Once a resident became a teacher, the probabilities for him/her to continue being a teacher or become a farmer, butcher, baker or doctor would be 10%, 40%, 30%, 20% and 0%, respectively.


5. Once a resident became a doctor, the probabilities for him/her to continue being a doctor is 100%.

Use the above given information to complete the following works:

1. Carefully present a model to describe the given information.


2. Calculate the probabilities of grandparents and grandchildren in that village making the same job choices.


3. Suppose many generations of the villagers are now studied by using your model. When the studied generation number,n, goes toinfinity, what predictions could you make about the numbers of people working at those jobs?