This preview shows pages 1–18. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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?...
View Full
Document
 Fall '11
 Rau

Click to edit the document details