lec-25 - Administration I have regraded midterms. Come get...

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Unformatted text preview: Administration I have regraded midterms. Come get them after class. CS70: Satish Rao: Lecture 25. 1. Distribution Comparison 2. Poisson Application 3. Variance Distributions: continued. Pr [ X = i ] = ( e- 4 ) 4 i i ! E [ X ] = 4 = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 Pr [ X = i ] = ( 10 i ) ( . 4 ) i ( . 6 ) 10- i E [ X ] = 4 n = 10 , p = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 p = . 25 Pr [ X = i ] = . 75 i- 1 . 25 E [ X ] = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 Poisson and binomial.. Poisson: balls in bin 1 when n balls into n / bins. Binomial: n , p = n . In the limit of large n , Binomial converges to Poisson. Poisson and binomial.. Poisson: balls in bin 1 when n balls into n / bins. Binomial: n , p = n . In the limit of large n , Binomial converges to Poisson. How big a server? 1. Say 14,400 requests arrive in an hour? 2. Each request takes a second to process. How many servers should you have to keep up? How big a server? 1. Say 14,400 requests arrive in an hour? 2. Each request takes a second to process. How many servers should you have to keep up? 14400 / 3600 = 4 How big a server? 1. Say 14,400 requests arrive in an hour? 2. Each request takes a second to process. How many servers should you have to keep up? 14400 / 3600 = 4 So four servers? Modeling: How big a server? 1. n customers, n is unknown. 2. Each makes request with (small) probability p . (Rare Event.) Dont know n and p . Modeling: How big a server? 1. n customers, n is unknown. 2. Each makes request with (small) probability p . (Rare Event.) Dont know n and p . Cant use binomial. Modeling: How big a server? 1. n customers, n is unknown. 2. Each makes request with (small) probability p . (Rare Event.) Dont know n and p . Cant use binomial. Use Poisson! Modeling: How big a server? 1. n customers, n is unknown. 2. Each makes request with (small) probability p . (Rare Event.) Dont know n and p . Cant use binomial. Use Poisson! With = 14 , 400 / 3 , 600 =4. Poisson and servers. Pr [ X = i ] = ( e- 4 ) 4 i i ! E [ X ] = 4 = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 Poisson and servers. Pr [ X = i ] = ( e- 4 ) 4 i i ! E [ X ] = 4 = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 Can I usually keep up with the load? Poisson and servers. Pr [ X = i ] = ( e- 4 ) 4 i i ! E [ X ] = 4 = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 Can I usually keep up with the load? What is Pr [ X number of servers ] ? Poisson and servers. Pr [ X = i ] = ( e- 4 ) 4 i i ! E [ X ] = 4 = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 Can I usually keep up with the load? What is Pr [ X number of servers ] ? i Pr [ X i ] 4 . 628 Poisson and servers. Pr [ X = i ] = ( e- 4 ) 4 i i ! E [ X ] = 4 = 4 1 2 3 4 5 6 7 8 9 10 . 1 . 2 Can I usually keep up with the load?...
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lec-25 - Administration I have regraded midterms. Come get...

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