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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 onehour 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)=1P(X 1)=1P(X=0)P(X=1) P(X>1)=10.1350.271=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 ....
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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.
 Spring '09
 NegarKayavash

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