Problem 1. Hidden Markov Models and Protein Structure. (20 pts) One biological application of hidden Markov models is to determine the secondary structure (i. e. the general three dimensional shape) of a protein. This general shape is made up of alpha helices, beta sheets, turns and other structures. In this problem we will assume that the amino acid composition of these regions is governed by an HMM. In order to keep this problem relatively simple, we do not use actual transition values or emission probabilities. We will use the state transition probabilities of