Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C1), Frenzy (C2), and Tremor (C3).A transition matrix, indicating the probability that a resident in one city will travel to another, is given below.Cuthbert's job is to schedule the required number of seats, one to each person making the trip (transition), on a daily basis.
C F T
Transition matrix:

π(0)= [100, 100, 100]
-Using the data given in Table 14-4, how many people can we expect to find in each city tomorrow evening?
A)Chaos = 90, Frenzy = 110, Tremor = 100
B)Chaos = 110, Frenzy = 100, Tremor = 90
C)Chaos = 80, Frenzy = 90, Tremor = 130
D)Chaos = 100, Frenzy = 130, Tremor = 70

Question

Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C1), Frenzy (C2), and Tremor (C3).A transition matrix, indicating the probability that a resident in one city will travel to another, is given below.Cuthbert's job is to schedule the required number of seats, one to each person making the trip (transition), on a daily basis.
C F T
Transition matrix: 
 
π(0)= [100, 100, 100]
-Using the data given in Table 14-4, how many people can we expect to find in each city tomorrow evening?
A)Chaos = 90, Frenzy = 110, Tremor = 100 
B)Chaos = 110, Frenzy = 100, Tremor = 90 
C)Chaos = 80, Frenzy = 90, Tremor = 130 
D)Chaos = 100, Frenzy = 130, Tremor = 70

Quizplus · Accepted Answer

To find the expected number of people in each city tomorrow evening, we need to multiply the transition matrix with the current population vector, π(0).
The resulting vector will be the expected population vector, π(1).
π(1) = [0.7 0.3 0] [100 100 100] = [90 110 100]
Therefore, we can expect to find 90 people in Chaos, 110 people in Frenzy, and 100 people in Tremor tomorrow evening. 
This matches option B.

Table 14-4 Cuthbert Wylinghauser Is a Scheduler of Transportation for the State