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# hw12 - CS 70 Spring 2005 Discrete Mathematics for CS...

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CS 70 Discrete Mathematics for CS Spring 2005 Clancy/Wagner HW 12 Due Thursday, April 28 Coverage: This assignment involves topics from the lectures of April 19 and 21, and from Rosen section 5.3. Administrative reminders: We will accept only unformatted text files or PDF files for homework sub- mission. Include your name, login name, section number, and partner list in your submission. Give the command submit hw12 to submit your solution to this assignment. Homework exercises: 1. (8 pts.) Independence (a) Show that, for independent random variables X , Y , we have E [ XY ] = E [ X ] × E [ Y ] . H INT : Show first—carefully!—that, even if the random variables are not independent, E [ XY ] = a b ab × Pr [ X = a Y = b ] . (b) Give a simple example to show that the conclusion of the previous part is not necessarily true when X and Y are not independent. 2. (16 pts.) Those 3407 Votes In the aftermath of the 2000 US Presidential Election, many people have claimed that the 3407 votes cast for Pat Buchanan in Palm Beach County are statistically highly significant, and thus of dubious validity. In this problem, we will examine this claim from a statistical viewpoint. The total percentage votes cast for each presidential candidate in the entire state of Florida were as follows: Gore Bush Buchanan Nader Browne Others 48.8% 48.9% 0.3% 1.6% 0.3% 0.1% In Palm Beach County, the actual votes cast (before the recounts began) were as follows: Gore Bush

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