The Tiger Sports Shop1 has hired you as an analyst to understand its market position with respect to Clemson merchandise. It is particularly concerned about its major competitor, Mr. Knickerbocker, and which Clemson-related store has the ‘lead’ market share. Recent history has suggested that which Clemson-related store has the ‘lead market share’ can be modeled as a Markov Chain using three states: TSS (Tiger Sports Shop), MK (Mr. Knickerbocker), and Other Company (OC). Data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data in the picture. a) The current state of the lead market share in October is that Tiger Sports Shop is in the lead (i.e., the Markov Chain in October is TSS). Tiger Sports Shop is considering launching a new brand in February only if it has the lead market share in January. Determine the probability that TSS will launch this new brand. Please show any equations or matrices used to calculate this probability. (b) Provide the steady-state equations and calculate the steady-state probabilities for the Markov Chain. (c) The Tiger Sports Shop makes total revenues of $125,000 if it is in the lead market share during a month; $80,000 if MK (Mr. Knickerbocker) is in the lead market share during a month; and $50,000 if the other company is in the lead market share during a month. Determine the expected total revenue per month of the Tiger Sports Shop.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Tiger Sports Shop1 has hired you as an analyst to understand its market position with respect to Clemson merchandise. It is particularly concerned about its major competitor, Mr. Knickerbocker, and which Clemson-related store has the ‘lead’ market share. Recent history has suggested that which Clemson-related store has the ‘lead market share’ can be modeled as a Markov Chain using three states: TSS (Tiger Sports Shop), MK (Mr. Knickerbocker), and Other Company (OC). Data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data in the picture. a) The current state of the lead market share in October is that Tiger Sports Shop is in the lead (i.e., the Markov Chain in October is TSS). Tiger Sports Shop is considering launching a new brand in February only if it has the lead market share in January. Determine the probability that TSS will launch this new brand. Please show any equations or matrices used to calculate this probability. (b) Provide the steady-state equations and calculate the steady-state probabilities for the Markov Chain. (c) The Tiger Sports Shop makes total revenues of $125,000 if it is in the lead market share during a month; $80,000 if MK (Mr. Knickerbocker) is in the lead market share during a month; and $50,000 if the other company is in the lead market share during a month. Determine the expected total revenue per month of the Tiger Sports Shop.

The image displays a table of transition probabilities among three states: TSS, MK, and OC. The rows represent the current state, while the columns represent the next state. Each cell contains the probability of transitioning from one state to the other.

- The probability of staying in the TSS state is 0.75, transitioning from TSS to MK is 0.15, and from TSS to OC is 0.10.
- The probability of transitioning from MK to TSS is 0.30, staying in MK is 0.60, and transitioning from MK to OC is 0.10.
- The probability of transitioning from OC to TSS is 0.20, from OC to MK is 0.10, and staying in OC is 0.70.

This table might be used to model a Markov chain, representing the likelihood of moving between these states.

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