Chapter 14 Markov Analysis

51) Using the data in Table 14-1, determine Company 2's estimated market share in the next period.

A) 0.26

B) 0.27

C) 0.28

D) 0.29

E) None of the above

52) Using the data in Table 14-1, and assuming that the transition probabilities do not change, in the long run what market share would Company 2 expect to reach? (Rounded to two decimal places.)

A) 0.30

B) 0.32

C) 0.39

D) 0.60

E) None of the above

53) The weather is becoming important to you since you would like to go on a picnic today. If it was sunny yesterday, there is a 70% chance it will be sunny today. If it was raining yesterday, there is a 30% chance it will be sunny today. What is the probability it will be rainy today, if it was sunny yesterday?

A) 0.1

B) 0.2

C) 0.7

D) 0.8

E) 0.3

54) The initial values for the state probabilities

A) are always greater than the equilibrium state probabilities.

B) are always less than the equilibrium state probabilities.

C) do not influence the equilibrium state probabilities.

D) heavily influence the equilibrium state probabilities.

E) None of the above

55) The matrix that is needed to compute equilibrium conditions when absorbing states are involved is called a(n)

A) transition matrix.

B) fundamental matrix.

C) identity matrix.

D) equilibrium matrix.

E) absorbing matrix.

56) The weather is becoming important to you since you would like to go on a picnic today. If it was sunny yesterday, there is a 70% chance it will be sunny today. If it was raining yesterday, there is a 30% chance it will be sunny today. If the probability that it was raining yesterday is 0.25, what is the probability that it will rain today?

A) 0.1

B) 0.3

C) 0.4

D) 0.7

E) None of the above

57) The weather is becoming important to you since you would like to go on a picnic today. If it was sunny yesterday, there is a 65% chance it will be sunny today. If it was raining yesterday, there is a 30% chance it will be sunny today. If the probability that it was raining yesterday is 0.4, what is the probability that it will be sunny today?

A) 0.650

B) 0.390

C) 0.510

D) 0.490

E) None of the above

Table 14-2

The following data consists of a matrix of transition probabilities (P) of three competing retailers, the initial market share ?(0). Assume that each state represents a retailer (Retailer 1, Retailer 2, Retailer 3, respectively) and the transition probabilities represent changes from one month to the next.

P = ?(0) = (0.3, 0.6, 0.1)

58) Using the data given in Table 14-2, find the market shares for the three retailers in month 1.

A) ?(1) = (0.09, 0.42, 0.49)

B) ?(1) = (0.55, 0.33, 0.12)

C) ?(1) = (0.18, 0.12, 0.70)

D) ?(1) = (0.55, 0.12, 0.33)

E) ?(1) = (0.33, 0.33, 0.33)

59) Using the data given in Table 14-2, find the market shares for the three retailers in month 2.

A) ?(2) = (0.30, 0.60, 0.10)

B) ?(2) = (0.55, 0.33, 0.12)

C) ?(2) = (0.44, 0.43, 0.12)

D) ?(2) = (0.55, 0.12, 0.33)

E) ?(2) = (0.47, 0.40, 0.13)

60) Using the data given in Table 14-2, what is the equilibrium market share?

A) (0.30, 0.60, 0.10)

B) (0.55, 0.33, 0.12)

C) (0.44, 0.43, 0.12

D) (0.55, 0.12, 0.33)

E) (0.47, 0.40, 0.13)

61) Using the data given in Table 14-3, how many employees do we expect in location A one year from now?

A) 1000

B) 1400

C) 1500

D) 800

E) 700

62) 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

E) 820

63) Using the data given in Table 14-3, how many employees do we expect in location B one year from now?

A) 1000

B) 1400

C) 1500

D) 800

E) 700

64) Using the data given in Table 14-3, how many employees do we expect in location B two years from now?

A) 1000

B) 1400

C) 1420

D) 1500

E) 820

65) Using the data given in Table 14-3, what is the long run number of employees expected in location C?

A) 1400

B) 1000

C) 800

D) 750

E) 700

66) Using the data given in Table 14-4, how many seats should Cuthbert schedule for travel from Chaos to Tremor for tomorrow?

A) 80

B) 70

C) 20

D) 60

E) None of the above

67) 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

68) Using the data given in Table 14-4, find the equilibrium travel population for Frenzy (rounded to the nearest whole person).

A) 126

B) 95

C) 79

D) 100

E) None of the above

69) Using the data given in Table 14-4, what is the equilibrium travel population of Chaos (rounded to the nearest whole person)?

A) 79

B) 95

C) 126

D) 100

E) None of the above

70) A certain utility firm has noticed that a residential customer's bill for one month is dependent on the previous month's bill. The observations are summarized in the following transition matrix.