5. Moving Books Arround You have N books on your shelf, labelled 1, 2, ..., N. You pick a book j with probability 1/N. Then you place it on the left of all others on the shelf. You repeat the process, independently. Construct a Markov chain which takes values in the set of all N! permutations of the books. (a) Find the transition probabilities of the Markov chain. (b) Find its stationary distribution. Hint: You can guess the stationary distribution before computing it