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 8.18.5 in Textbook)
Problem 1
Nefeli, a student in a probability class, takes a multiplechoice 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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 Spring '07
 BARD
 Normal Distribution, Standard Deviation, Probability theory, Mean squared error

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