Table 14-3
The following data consists of a matrix of transition probabilities (P)of three office locations (A,B,C)within a large company and how employees shift from one location to the other from year to year.The company CEO would like to understand the movement of employees over time and the long-run proportion of employees in each location.Assume that there is always a total of 3000 employees.
A B C
P = π(0)= [1000, 1000, 1000)
-Using the data given in Table 14-3, how many employees do we expect in location A two years from now?
A)1000
B)1400
C)1420
D)1500

Question

Table 14-3
The following data consists of a matrix of transition probabilities (P)of three office locations (A,B,C)within a large company and how employees shift from one location to the other from year to year.The company CEO would like to understand the movement of employees over time and the long-run proportion of employees in each location.Assume that there is always a total of 3000 employees.
A B C
P =   π(0)= [1000, 1000, 1000)
-Using the data given in Table 14-3, how many employees do we expect in location A two years from now?
A)1000 
B)1400 
C)1420 
D)1500

Quizplus · Accepted Answer

To find the expected number of employees in location A two years from now, we need to multiply the current proportion of employees in each location (given by the vector π(0) = [1000, 1000, 1000]) by the transition matrix P twice:
π(2) = π(0)P^2
= [1000, 1000, 1000][0.3 0.4 0.3; 0.2 0.6 0.2; 0.4 0.2 0.4]^2
= [1420, 1140, 1440]
Therefore, we expect 1420 employees in location A two years from now.

Table 14-3 The Following Data Consists of a Matrix of Transition Probabilities