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Write at least two different ways that the joint probability p(X,Y,Z) could be broken down into a product of  three probabilities using the chain rule.
 
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The naïve Bayes classifier is so called because it makes a series of very naïve conditional independence assumptions.  What are they?
 
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Give three examples of information retrieval systems or information retrieval tasks you've used a computer to perform.
 
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A system designed to find photos that include animals out of a store of nature photos found 15 of the animal photos and correctly identified 115 of the animal-free nature photos as not having animals; but it marked 5 photos as having animals when they didn't, and missed 10 of the photos that did have animals.  What are the precision and recall of this system?
 
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If I wanted to build a system that could guarantee 100% recall, how could I trivially do that?