Introduction to Bioinformatics - Assignment 3 Problems | BCB 444, Assignments of Bioinformatics

Download Introduction to Bioinformatics - Assignment 3 Problems | BCB 444 and more Assignments Bioinformatics in PDF only on Docsity! BCB 444/544 Fall 07 Sept 24 HW3 p1of 2 BCB 444/544 Homework 3 (20pts) Name _________________________________________ Due Mon Oct 8 by 5 pm (please bring to class or deliver to MBB 106) Objectives: 1. Practice using hidden Markov models to compute probabilities Notes: You may work together on these problems, but each student must submit answers in his/her own words. It's always best to show all of your calculations & intermediate steps. Introduction: We learned about hidden Markov models in class, but its difficult to really understand how they work until you have some practice working with them. This homework will give you practice calculating probabilities from an HMM. It isn’t a bioinformatics example problem, but this model will be much easier to work through with by hand. You can write some code to handle the more complicated biological models on your own time.  1. Consider the occasionally dishonest casino example discussed in class. The system has 3 states: B denotes the start state F denotes the state when a fair die is used L denotes the state when a loaded die used The transition probabilities between these states are shown in the diagram. The emission probabilities are: for state F, eF(1) = eF(2) = … = eF(6) = 1/6; for state L, eL(1) = eL(2) = … = eL(5) = 0.1, eL(6) = 0.5 a) (5 pts) Calculate the probability: What is the probability of the sequence (6, 1, 3) given that a fair die was used for all three rolls? What is the probability of the sequence (6, 1, 3) given that a loaded die was used for all three rolls?