hw8sol

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 2 Consider the following Bayesian network: a) Are D and E necessarily independent given evidence about both A and B?
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online