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ps1 - Introduction to Probabilistic Graphical Models...

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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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