hw8sol

# hw8sol - CS4600 Introduction to Intelligent Systems Fall...

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CS4600 - Introduction to Intelligent Systems Fall 2000 Homework 9 - Sample Solution Problem 1 Of the entire population, 2% has a certain disease X. A test Y, which indicates whether or not a person has the disease, is not 100% accurate. If a person has the disease, there is a 6% chance that it will go undetected by the test. However, there is also a 9% chance of "false alarm" (meaning that the person does not have the disease but the test indicates otherwise). A person Z takes a test which later comes out positive (meaning that the test says he has the disease). What is the proba- bility of this person having the disease in reality? Let D be"having the disease" + be "test positive" We are given the following information: P(D) = 0.02 which implies P(not D) = 0.98 P(not + | D) = 0.06 which implies P(+ | D) = 0.94 P(+ | not D) = 0.09 First, we compute P(+) = P(+ AND D) + P(+ AND (not D)) = P(+ | D) P(D) + P(+ | not D) P(not D) = 0.94 x 0.02 + 0.09 x 0.98 = 0.107 We would like to know P(D | +) = P(+ | D) x P(D) / P(+) = 0.94 x 0.02 / 0.107 ~= 0.1757

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Problem 2 Consider the following Bayesian network: a) Are D and E necessarily independent given evidence about both A and B?
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hw8sol - CS4600 Introduction to Intelligent Systems Fall...

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