3.2.3 Suppose the Purpose-flea is equally likely to start at any base point at time zero, find the probability distribution of $X_1$.
3.2.4 Suppose the Purpose-flea begins at base point 1 at time zero, find the probability distribution of $X_2$.
3.2.5 Suppose the Purpose-flea is equally likely to start at any base point at time zero. Find the probability of obtaining the course (3, 2, 1, 1, 3).
3.3 Consider the Markov chain with transition diagram below:
[Diagram]
3.3.1 Which classes communicate? Why?
3.3.2 Is the Markov chain irreducible, absorbing. Why?
3.3.3 Which states are recurrent? Give reasons.
3.3.4 Which states are transient? Give reasons.