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5. Consider a continuous time Markov chain with states 1,2,3,4. From 1 it jumps to any of the other states at rate 1 each. From 2 it jumps to 3 at rate 2 and to 4 at rate 1. From 3 it jumps to 1 or 4 at rate 1 and to 2 at rate 2. From 4 it can only jump to 3, and does that at rate 1.
a) Draw the graph for this chain and write down the rates matrix (also known as the infinitesimal generator of the Markov chain).
(b) Find the stationary distribution.
(c) Suppose the chain starts in state 1. What is the expected amount of time it requires to jump away from that state? Why?