CS 440: Introduction to AI
Homework 4
Due: November 9 11:59PM, 2010
Your answers must be concise and clear.
Explain sufficiently that we can
easily determine what you understand.
We will give more points for a brief
interesting discussion with no answer than for a bluffing answer.
Please email your solution to the TA at [email protected]
1
Probability
1. Consider a joint probability distribution
P
(
X, Y, Z
) over variables X, Y,
and Z. Assume that the probability of each outcome is nonzero. Is the
following equation always true? Prove its correctness or incorrectness.
P
(
X

Y, Z
) =
P
(
Y

X,Z
)
P
(
X

Z
)
P
(
Y

Z
)
2. After your yearly checkup, the doctor has bad news and good news. The
bad news is that you tested positive for a serious disease and that the test
is 95% accurate (i.e., the probability of testing positive when you have the
disease is 0.95 and the probability of testing negative when you don’t have
the disease is 0.95). The good news is that this is a rare disease, striking
only 1 in 100,000 individuals.
Why is it good news that the disease is
rare? What are the chances that you actually have the disease?
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 Spring '08
 Levinson
 Artificial Intelligence, Probability, Probability theory, Bayesian probability, Bayesian network, ChowLiu tree

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