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Homework 8

# Homework 8 - EE 351K PROBABILITY RANDOM PROCESSES FALL 2011...

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EE 351K PROBABILITY & RANDOM PROCESSES FALL 2011 Instructor: Sujay Sanghavi [email protected] Homework 8 Due: November 2nd, 4:00pm (dropping it to mailbox @ENS 431) Focus: Bayesian Inference (Section 8.1-8.5 in Textbook) Problem 1 Nefeli, a student in a probability class, takes a multiple-choice test with 10 questions and 3 choices per question. For each question. there are two equally likely possibilities, independent of other questions: either she knows the answer, in which case she answers the question correctly. or else she guesses the answer with probability of success 1/3. (a) Given that Nefeli answered correctly the first question, what is the probability that she knew the answer to that question? (b) Given that Nefeli answered correctly 6 out of the 10 questions, what is the posterior PMF of the number of questions of which she knew the answer? Problem 2 Suppose points in R are being obtained from two classes, C 1 and C 2 , both of which are normally distributed with parameters (1 , 1) and ( - 1 , 1) respectively. If it is known that the priors of

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Homework 8 - EE 351K PROBABILITY RANDOM PROCESSES FALL 2011...

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