Lec-27 - Administration I have regraded midterms Come get them after class CS70 Satish Rao Lecture 27 1 Chebyshevs inequality(Markovs inequality 2

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CS70: Satish Rao: Lecture 27. 1. Chebyshev’s inequality. (Markov’s inequality. 2. Polling.
Variance! What is it good for?!? Absolutely. .. something!

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What do we want to bound? Recall the number of servers problem? Average request rate: 4 X - number of requests. Number of servers: 10 will be enough with prob. . 997 . That is, Pr [ X > 10 ] < . 003 . Pr [ X = i ] = ( e - 4 ) 4 i i ! E [ X ] = 4 λ = 4 0 1 2 3 4 5 6 7 8 9 10 0 . 1 . 2
Plotting Pr [ X > α ] Pr [ X i ] 0 1 2 3 4 5 6 7 8 9 10 0 . 5 1

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Average request rate: 100 X - number of requests. Number of servers: 130 will be enough with prob. 135 . That is, Pr [ | X - 100 | > 30 ] < . 01 Pr [ X i ] λ = 100 0 15 30 45 60 75 90 105 120 135 150 0 . 5 1

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Bound Pr [ | X - μ | > α ] ! Chebyshev’s Inequality: For a random variable X with expectation μ Pr [ | X - μ | ≥ α ] Var ( X ) α 2 . Corollary:
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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.

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Lec-27 - Administration I have regraded midterms Come get them after class CS70 Satish Rao Lecture 27 1 Chebyshevs inequality(Markovs inequality 2

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