| 0.7 0.15 |
| 0.3 0.85 |
This matrix shows the transition probabilities from one type of computer to another. The first row represents the probability of staying with the same type of computer (0.7 for Mac and 0.85 for PC), while the second row represents the probability of switching to the other type of computer (0.3 for Mac and 0.15 for PC).
To find the long-term distribution of computer usage among the employees, we can use the eigenvector corresponding to the eigenvalue of 1 for the migration matrix. This will give us the proportion of employees using each type of computer in the long run.
The eigenvector equation for the migration matrix M is given by:
(M - I)v = 0
Where M is the migration matrix, I is the identity matrix, and v is the eigenvector we are trying to find.
Solving this equation will give us the long-term distribution of computer usage among the employees.