MIT6_042JF10_rec20

MIT6_042JF10_rec20 - 6.042/18.062J Mathematics for Computer...

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Unformatted text preview: 6.042/18.062J Mathematics for Computer Science November 24, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 20 Suppose that a coin that comes up heads with probability p is flipped n times. Then for all α < p 1 − α 2 nH ( α ) Pr { # heads ≤ αn } ≤ 1 − α/p · 2 πα (1 − α ) n · p αn (1 − p ) (1 − α ) n where: 1 1 H ( α ) = α log 2 α + (1 − α ) log 2 1 − α 1 Approximating the Cumulative Binomial Distribu- tion Function A coin that comes up heads with probability p is flipped n times. Find an upper bound on Pr { # heads ≥ βn } where β > p . Think about the number of tails and plug into the monster formula above. Recitation 20 2 2 Gallup’s Folly A Gallup poll found that 45% of the adult population of the United States plan to vote Republican in the next election. Gallup polled 640 people and claims a margin of error of 3 percentage points....
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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_rec20 - 6.042/18.062J Mathematics for Computer...

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