Reference no: EM133179581

Question - SUM is one of the leading smartphone manufacturers, and it has recently developed a new flagship smartphone. In the high-end smartphone market, SUM has two main competitors: APP and HUA. SUM is investigating customer behaviour in the market, and wishes to see that customers who bought SUM's smartphone also purchase its products next time.

Market research shows that Of those who bought SUM, 70% buy it again, 20% change to APP and 10% change to HUA.

Of those who bought APP, 60% buy it again, 20% change to SUM and 20% change to HUA.

Of those who bought HUA, 50% buy it again, 30% change to SUM and 20% change to APP

i. Write down the transition probability matrix of purchases.

ii. The current high-end smartphone market share for SUM is 30%, and those with APP and HUA are 40% and 30% respectively. Predict the market share after a period of two years using the transition probability matrix, taking into account the fact that a typical customer purchases a new smartohone ever two years.

iii. Given the transition probability matrix of purchases in (i) and the current market share in (ii), construct a system of linear equations, and estimate the market share of SUM, APP and HUA two years ago using the matrix method.