Question

2. A stochastic process on a stable population P is described by the following system of equations. 5 3 1+1 ti + 10 10 5 7 Yi+1 Ii + 10 10 An interpretation of this system might be that on day i of semester 2, 1; students do not enjoy kma154 and y, students enjoy it. On the following day, 50% of the students who disliked kma154 continue to dislike it and 50% change their mind. Similarly, 70% of the students who liked kma154 continue to like it and 30% change their mind. 5/10 3/10 The transition probabilities can be summarised in a Markov matrix M 5/10 7/10 7 5 3 10 36 With M2 = MM GO compute Mº and MⓇ in a simi- 5 7 5 7 60 61 5 % - 10 5 2 100 lar way. Subsequently, predict the steady state distribution of this system at the end of semester.

Answer 1

3 5. 3/10 M= 15/0 5/10 10 710 5 7 0.4 0.36 40 36 M2= too 6064 M = M² M²= [ Home List 0.6 0.64 3760 3744 0.376 0.3744 6240 6256 0.624 0.6256 874999 o a M8. MY MY 137500160 1 108 6 2499890, 6250096 0.37500160 0.3749904 0.62499840 0.6250096 Prediction of steady state distribution, Lam M n 10.375 0.375 hVx) 0.625 0.625 Hence 62.5% student will be like the course 37.5% student will dislike the course.