1. ((a) - Class 9,(b,c) Class 10)[30 points] The Tiger Sports Shop 1 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: 1 This was the first place I bought anything Clemson-related and they gave me rewards point, so my family and I Tiger Sports Shop people. 1 Please address the following questions: (a) [10 points] 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) [15 points] Provide the steady-state equations and calculate the steady-state probabilities for the Markov Chain. (c) [5 points] 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