MIT6_042JF10_rec19

MIT6_042JF10_rec19 - 6.042/18.062J Mathematics for Computer...

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Unformatted text preview: 6.042/18.062J Mathematics for Computer Science November 19, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 19 1 Bayes Rule Bayes Rule says that if A and B are events with nonzero probabilities, then: Pr { A | B } Pr { B } = Pr { B | A } Pr { A } a. Prove Bayes Rule. b. A weatherman walks to work each day. Some days it rains: Pr { rains } = 0 . 30 Sometimes the weatherman brings his umbrella. Usually this is because he predicts rain, but he also sometimes carries it to ward off bright sunshine. Pr { carries umbrella } = 0 . 40 As a weatherman, he usually doesnt get caught out in a storm without protection: Pr { carries umbrella | rains } = 0 . 80 Suppose you see the weatherman walking to work, carrying an umbrella. What is the probability of rain? Use Bayes Rule. Recitation 19 2 2 DNA Profiles Suppose that we create a a national database of DNA profiles. Lets make some (overly) simplistic assumptions: Each person can be classified into one of 20 billion...
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This note was uploaded on 01/19/2012 for the course CS 6.042J / 1 taught by Professor Tomleighton,dr.martenvandijk during the Fall '10 term at MIT.

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MIT6_042JF10_rec19 - 6.042/18.062J Mathematics for Computer...

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