7. A company is considering using Markov theory to analyse consumers switching between the five different brands of washing aids which it markets. All of these washing aids are designed to make washed clothes clean and fresh, but use different approaches. Two of these aids (A and B), are powder based. A further two (C and D), are based on liquid filled tablets. The final aid (E) is just liquid based. The current market shares for the five washing aids are 10%, 20%, 35%, 25% and 10% for aids A,B,C,D and E respectively. Market research has produced the data shown below for the probability of customers switching between washing aids every six months. To washing aid A B C D E From A 1 0 0 0 0 washing B aid 0.37 0.17 0.07 0.39 0 C 0 0 1 0 0 D 0.38 0.20 0.13 0.29 0 E 0 0 0 1 0 Here, for example, there is a probability of 0.07 that a customer switches from aid B to aid C. (a) Copy the following table into your answer and fill in the market shares for these brands after six months. A B C D E Market share (%, 2dp)
7. A company is considering using Markov theory to analyse consumers switching between the five different brands of washing aids which it markets. All of these washing aids are designed to make washed clothes clean and fresh, but use different approaches. Two of these aids (A and B), are powder based. A further two (C and D), are based on liquid filled tablets. The final aid (E) is just liquid based. The current market shares for the five washing aids are 10%, 20%, 35%, 25% and 10% for aids A,B,C,D and E respectively. Market research has produced the data shown below for the probability of customers switching between washing aids every six months. To washing aid A B C D E From A 1 0 0 0 0 washing B aid 0.37 0.17 0.07 0.39 0 C 0 0 1 0 0 D 0.38 0.20 0.13 0.29 0 E 0 0 0 1 0 Here, for example, there is a probability of 0.07 that a customer switches from aid B to aid C. (a) Copy the following table into your answer and fill in the market shares for these brands after six months. A B C D E Market share (%, 2dp)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:7.
A company is considering using Markov theory to analyse consumers switching
between the five different brands of washing aids which it markets. All of these
washing aids are designed to make washed clothes clean and fresh, but use
different approaches. Two of these aids (A and B), are powder based. A further
two (C and D), are based on liquid filled tablets. The final aid (E) is just liquid
based.
The current market shares for the five washing aids are 10%, 20%, 35%, 25%
and 10% for aids A,B,C,D and E respectively. Market research has produced
the data shown below for the probability of customers switching between
washing aids every six months.
To washing aid
A
B
C
D
E
From A
1
0
0
0
0
washing B
aid
0.37
0.17
0.07
0.39
0
C
0
0
1
0
0
D
0.38
0.20
0.13
0.29
0
E
0
0
0
1
0
Here, for example, there is a probability of 0.07 that a customer switches from
aid B to aid C.
(a)
Copy the following table into your answer and fill in the market shares for
these brands after six months.
A B C D E
Market share (%, 2dp)
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