GE 331-Lecture 10 - IE 300/GE 331 Lecture 10 Negar...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IE 300/GE 331 Lecture 10 Negar Kiyavash, UIUC 1 Previous lecture Poisson process # of events that occur randomly in a time (spatial) unit is modeled by a Poisson r.v. X Average # of events in the time (spatial) unit is known as (arrival rate: arrivals/time unit) Poisosn process: the # of events X t occur in t time units ... 2 , 1 , , ! ) ( ) ( = = = = x e x x X P x f x ... 2 , 1 , , ! ) ( ) ( = = = x e x t x X P t x t IE 300/GE 331 Lecture 10 Negar Kiyavash, UIUC 2 Poisson distribution (cont) Example: The number of patients arriving at the emergency room of a local hospital is modeled as a Poisson r.v. Suppose patients arrive at the rate of 2 every 30 minutes. What is the probability that more than 1 patients arrive in 30 minutes? What is the probability that 4 patients arrive in an hour? What is the probability that in 4 one-hour periods, at least one of them has 4 patient arriving IE 300/GE 331 Lecture 10 Negar Kiyavash, UIUC 3 IE 300/GE 331 Lecture 10 Negar Kiyavash, UIUC 4 Poisson distribution (cont) Let X be the number of patients arriving in 30 minutes X has a Poisson distribution with parameter =2 Interested in P(X>1) P(X>1)=P(X=2)+P(X=3)+ Consider its complement: P(X>1)=1-P(X 1)=1-P(X=0)-P(X=1) P(X>1)=1-0.135-0.271=0.594 135 . 1 1 ! ) ( 2 = = = = e e X P 0.271 1 2 ! 1 ) 1 ( 2 1 = = = = e e X P IE 300/GE 331 Lecture 10 Negar Kiyavash, UIUC 5 Poisson distribution (cont) Probability that 4 patients arrive in an hour Unit is different! One hour = 2*(30 minutes) Let Y be the number of patients arriving in one hour 195 ....
View Full Document

This note was uploaded on 09/08/2009 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

Page1 / 23

GE 331-Lecture 10 - IE 300/GE 331 Lecture 10 Negar...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online