1. Suppose you are about to start working for Apple Corp. as an intern, so you do some research on the various job positions within the company. In your area of work, there are 4 basic positions that you can hold: intern, programmer, analyst, and project manager.

Each year there is a chance for promotion, and there is also a chance of "involuntary separation" from the company. (In other words, getting fired.)

If you are an intern, there is a 50% chance each year of being promoted to programmer, and a 10% of being fired.

If you are a programmer, there is a 12% chance each year of being promoted to analyst, and a 6% of being fired.

If you are an analyst, there is a 5% chance each year of being promoted to project manager, and a 3% of being fired.

If you are a project manager, you cannot be promoted but there is a 5% chance of being fired.

If you are not promoted or fired, then you stay in the same position. If you are fired, then you cannot be rehired.

What are the different states in this system?

Using excel, construct the transition matrix T for this system.Make sure to label the states.

Assuming you start working as an intern, what is the initial-state matrix ?

Find , , and for this system.

What is the probability that you will be an intern after 10 years?

What is the probability that you will be a project manger in 5 years?

What is the probability that you will be fired within 20 years?