The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. From/To A B C D Number of Customers A 0.2 0.3 0.1 0.4 2300 B 0 0.2 0.5 0.3 2800 C 0.3 0.5 0 0.2 2500 D 0.3 0.4 0.3 0 2400 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? c) What is the mean return time of Brand 1? Answer in 2 decimal places.
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. From/To A B C D Number of Customers A 0.2 0.3 0.1 0.4 2300 B 0 0.2 0.5 0.3 2800 C 0.3 0.5 0 0.2 2500 D 0.3 0.4 0.3 0 2400 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? c) What is the mean return time of Brand 1? Answer in 2 decimal places.
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. From/To A B C D Number of Customers A 0.2 0.3 0.1 0.4 2300 B 0 0.2 0.5 0.3 2800 C 0.3 0.5 0 0.2 2500 D 0.3 0.4 0.3 0 2400 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? c) What is the mean return time of Brand 1? Answer in 2 decimal places.
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. From/To A B C D Number of Customers A 0.2 0.3 0.1 0.4 2300 B 0 0.2 0.5 0.3 2800 C 0.3 0.5 0 0.2 2500 D 0.3 0.4 0.3 0 2400 a) What is the market share of Brand D in the long run? Answer in 2 decimal places.
b) How many customers will shift preference in using Brand C soap in the long run? c) What is the mean return time of Brand 1? Answer in 2 decimal places.
d) What is the percentage change of Brand B? Answer in 2 decimal places.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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