Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C 1 ),Frenzy (C 2 ),and Tremor (C 3 ).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 matix: 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
E)None of the above

Question

Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C 1 ),Frenzy (C 2 ),and Tremor (C 3 ).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 matix:   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 
E)None of the above

Quizplus · Accepted Answer

We can use the transition matrix and the initial distribution vector to calculate the expected number of people in each city tomorrow evening. We can do this by multiplying the transition matrix by the distribution vector. After one transition: [C₁ Frenzy] = [0.6 0.3 0.1] * [Chaos Frenzy Tremor] [C₂ Frenzy] = [0.2 0.7 0.1] * [Chaos Frenzy Tremor] [C₃ Frenzy] = [0.1 0.2 0.7] * [Chaos Frenzy Tremor] Multiplying these out, we get: [C₁ Frenzy] = [60 30 10]/100 * [100 100 100] = [60 30 10] [C₂ Frenzy] = [20 70 10]/100 * [100 100 100] = [20 70 10] [C₃ Frenzy] = [10 20 70]/100 * [100 100 100] = [10 20 70] So we can expect to find 60 people in Chaos, 30 people in Frenzy, and 10 people in Tremor tomorrow evening. Therefore, the answer is B) Chaos = 110, Frenzy = 100, Tremor = 90.

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