Introduction to Probabilistic Graphical Models Problem Set #11Probabilistic Graphical Models, Spring 2009Problem Set #1: Probability ReviewNote:In the questions below,Pis a joint probability distribution over the specified variables.For example,P(A, B|C) is a joint distribution over the variablesAandBgiven the variableC.Thus, for every possible value ofC, it specifies a probability distribution over all combinationsof values forAandB.1. After your yearly checkup, the doctor has bad news and good news.The bad news isthat you tested positive for a serious disease, and that the test is 99% accurate (i.e. theprobability of testing positive given that you have the disease is 0.99, as is the probabilityof testing negative given that you don’t have the disease). The good news is that this isa rare disease, striking only 1 in 10,000 people. Why is it good news that the disease israre? 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 ofsome general background evidence that remains fixed, rather than in the complete absence
This is the end of the preview.
access the rest of the document.
Probability theory, 99%, good news, ProbabiliTy Review