Question 4 (20 pts). WC wanders around 5 spots in NUS according to a CTMC with generator matrix LT1 LT7 NUH KR KV LT1 5 3 LT7 COH 2 -8 Q = NUH 0 0 KR 3 O -5 KV 3 1 Answer the followings. Note that the modifications in (c, d, e) are separate from each other, in the sense that each of them is a modification to the CTMC's generator matrix above. (a) (3 pts) Where does WC stay for the longest time in expectation, and what is the expected length of stay there? (b) (3 pts) After WC leaves KR, where will he mostly like be at? (c) (5 pts) Suppose that WC stays 3 times longer at LT7 in expectation, but the subsequent transition probabilities to other spots remain the same. Write down the generator matrix for this modified case. (d) (5 pts) Suppose that WC stays at LT1 for the same amount of expected time, but subsequently, he hops to another spot uniformly at random. Write down the generator matrix for this modified case. (e) (4 pts) Suppose that, upon visiting NUH, WC will stay there forever :( Write down the generator matrix for this modified case