sol.assig1 - Solutions for Assignment 1 Discrete...

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Solutions for Assignment 1 Discrete Mathematics II Macm 201 (Fall 2010) Section 3.5 Section 3.6
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faculty of science department of mathematics MACM 201 - D100A SSIGNMENT #1 Solution to the instructor question Solution comes from Dr. Cedric Chauve. 1. We recall Bayes’Theorem: Pr ( E | F )= Pr ( F | E ) Pr ( E ) Pr ( F ) . To prove it, we need to use the identity that relates the conditional probability of two events: Pr ( E F )= Pr ( F ) Pr ( E | F ) and by symmetry Pr ( E F )= Pr ( F E )= Pr ( E ) Pr ( F | E ) . By combining the two identities, we have that Pr ( F ) Pr ( E | F )= Pr ( E ) Pr ( F | E ) which implies Bayes’ Theorem. This theorem is fundamental in probabilities is at the heart of many optimization algorithms whose goal is to compute the maximum-likelihood solution of a problem described in a prob- abilistic framework. Such algorithms are central in many problems of computational biology, such as the ones based on bayesian Networks. Although the proof is very short, it requires a little bit of thinking to really understand it from
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sol.assig1 - Solutions for Assignment 1 Discrete...

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