Question

A company is using Markov theory to analyse switching between four different foods marketed as slimming aids. These slimming aids claim that with regular use they result in significant weight loss. Individual customers who buy these sliming aids only switch (on average) once every four months. Market research has produced the data shown below for the probability of customers switching between slimming aids. UL20/0468 Page 6 of 9 To 1 slimming aid From slimming aid 1234 1 0.04 0.02 0 0 0.55 0.89 0 0 0.30 0.04 0 0 0.11 0.05 1 2 3 4 Here, for example, there is a probability of 0.11 that a customer switches to slimming aid 4 from slimming aid 2. The current market shares are 9%, 78%, 3% and 10% for aids 1, 2, 3 and 4 respectively. (a) Copy the following table into your answer and fill in the long-run prediction for the market shares for these four slimming aids. Long-run (%, 2dp) Aid 1 Aid 2 Aid 3 Aid 4 (b) The appropriate regulatory authority in the country where these four slimming aids are marketed has been concerned about the claims made for weight loss. As a result of an investigation which they have made they intend to ban sliming aid 2 from the market in six months’ time for making false claims. Giving a clear explanation of your working, copy the following table into your answer and fill in the percentage of the market that will be affected by this ban when it is imposed in six months’ time. Value Percentage affected (2dp)

Answer 1