Introduction to Probabilistic Graphical Models Problem Set #1
1
Probabilistic Graphical Models, Spring 2009
Problem Set #1: Probability Review
Note:
In the questions below,
P
is a joint probability distribution over the specified variables.
For example,
P
(
A, B

C
) is a joint distribution over the variables
A
and
B
given the variable
C
.
Thus, for every possible value of
C
, it specifies a probability distribution over all combinations
of values for
A
and
B
.
1. 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 99% accurate (i.e. the
probability of testing positive given that you have the disease is 0.99, as is the probability
of testing negative given that you don’t have the disease). The good news is that this is
a rare disease, striking only 1 in 10,000 people. Why is it good news that the disease is
rare? What are the chances that you actually have the disease?
2. It is quite often useful to consider the effect of some specific propositions in the context of
some general background evidence that remains fixed, rather than in the complete absence
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 Fall '07
 EranSegal
 Probability theory, 99%, good news, ProbabiliTy Review

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