iii. A state is divided into 3 regions. It is found each year that 5% of those in region 1 move to region 2 and 5% move to region 3. Of the residents of region 2, 15% move to region 1 and 10% move to region 3. Finally, 10% of those in region 3 move to region 1 and 5% more move to region 2. Determine the transition matrix for the stochastic process. Why is it a Markov process? iv. Suppose that Canyon has 3 competing restaurants that are highly favored by students; a pizza place, a Thai place and a Mexican place. Of those that typically order Thai food one week, the following week 0.6 order Thai food, 0.3 order pizza and 0.1 order Mexican. Of those that ordered Mexican food, next week 0.5 will order pizza and 0.2 Thai. Of those that order pizza, the following week 0.8 order pizza again, 0.05 order Mexican and 0.15 will order Thai. Determine the transition matrix for the order proportions from one week to the next. Is this problem a Markov process? Why or why not?