The daily air quality in Waterloo can be modeled as a three-state Markov chain with state spate S = {G, M, D}, corresponding respectively to good, moderate and dangerous. Use the transition matrices below to answer the following questions: [0.8 0.1 0.17 0.69 0.19 0.12 0.62 0.25 0.13 P = 0.1 0.7 0.2 P2 = 0.23 0.58 0.19 P3 = 0.32 0.51 0.17 0.4 0.4 0.2 0.44 0.41 0.15 0.46 0.39 0.15 (a) If Monday and Tuesday were good, what is the probability that Thursday is dangerous? (b) If Monday was good, what is the probability that Thursday and Friday will be moderate? (c) If Monday and Wednesday were good, how likely is it that Tuesday was dangerous? (d) If Tuesday is good, how likely is it that Monday was and Wednesday will be moderate? (e) Today is Monday, and the air quality is dangerous. When do you expect the air quality to improve