sol.assig1

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

This preview shows pages 1–4. Sign up to view the full content.

Solutions for Assignment 1 Discrete Mathematics II Macm 201 (Fall 2010) Section 3.5 Section 3.6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online