A grasshopper hops between three flowers, labelled 1, 2, 3. It starts from flower 1. Once it arrives at a flower, it sits there for a period of time distributed exponentially with parameter 2. Then it...

A grasshopper hops between three flowers, labelled 1, 2, 3. It starts from flower 1. Once it arrives at a flower, it sits there for a period of time distributed exponentially with parameter 2. Then it makes a jump, as follows: if it is located on flower 1, it jumps to 2 or 3 with equal probability; if it is located at 2, it jumps to 3, and if it is at 3, it jumps to 2. (a) Model the grasshopper using a continuous-time Markov chain. Find the states, the initial distribution and the jump rates! (b) What is the probability that at time t the grasshopper will sit on the third flower?