RESEARCH OPERATION

QUESTION FIVE a) Explain the following terms used in a Markov process i. Absorbing state ii. iii. Steady state Transient state (6marks) b) A company is considering using Markov theory to analyze brand switching between three different brands of flash discs. A survey has been done to estimate the following transition matrix for the probability of moving between brands each month: From Brand iii) To Brand 1 2 3 1 0.80 0.10 0.10 2 0.03 0.95 0.02 3 0.20 0.05 0.75 The current month (month 1) market shares are 45%, 25% and 30% respectively. i) What will be expected shares after two months have elapsed? ii) What is the probability of a current brand B purchaser switching to brand A two periods from now? What is the long-run prediction for the expected market share for each of the three brands? (14 marks)