cse250ahw1

# cse250ahw1 - CSE 250A. Assignment 1 Out: Tue Sep 28 Due:...

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CSE 250A. Assignment 1 Out: Tue Sep 28 Due: Tue Oct 05 1.1 Conditioning on background evidence [RN 13.9] It is often useful to consider the impact of speciﬁc events in the context of general background evidence, rather than in the absence of information. (a) Denoting such evidence by E , prove the conditionalized version of the product rule: P ( X,Y | E ) = P ( X | Y,E ) P ( Y | E ) . (b) Also, prove the conditionalized version of Bayes rule: P ( X | Y,E ) = P ( Y | X,E ) P ( X | E ) P ( Y | E ) . 1.2 Conditional independence [RN 13.10] Show that the following three statements about random variables X , Y , and Z are equivalent: P ( X,Y | Z ) = P ( X | Z ) P ( Y | Z ) P ( X | Y,Z ) = P ( X | Z ) P ( Y | X,Z ) = P ( Y | Z ) You should become ﬂuent with all these ways of expressing that X is conditionally independent of Y given Z . 1.3 Creative writing Attach events to the binary random variables X , Y , and Z that are consistent with the following patterns of commonsense reasoning. You may use different events for the different parts of the problem.

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## This note was uploaded on 11/20/2010 for the course CSE 250a taught by Professor Lawrence during the Spring '10 term at UCSD.

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cse250ahw1 - CSE 250A. Assignment 1 Out: Tue Sep 28 Due:...

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