Question 1 Three mobile phone brands A, B and C are in competition on the market. The results obtained from a survey carried out on a representative sample indicate that: On average, 50% of customers who have used brand A during one year buy the same brand the following year, while 25% of these customers buy brand B. Among B's customers, 50% continue to use B and 30% change to A. Among the customers of C, there is an equiprobability to buy the next phone from A or from C. 1. Explain why customers' behavior can be represented by a Markov chain. 2. Provide its transition matrix. 3. Given that Mohamed's last three phones are from brand A, say which brand Mohamed is most likely to buy his next phone from. Justify your answer. 4. Calculate the probability P(X+1B, X+2B, X+3=B/X=A). 5. Find the average time taken by a customer to buy back a phone from A? 6. Find the average time taken for a user to go from A to C? 7. Find the market share of each brand?