Poisson (ISE 484) - 1 Exponential Distribution& Poisson...

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: 1 Exponential Distribution & Poisson Process Memorylessness & other exponential distribution properties; Poisson process and compound P.P.’s 2 Exponential Distribution: Basic Facts Pr{ T ≤ t ) = ∫ t λ e – λ u d u = 1 – e – λ t ( t ≥ 0) f ( t ) = { λ e – λ t , t ≥ 0, t < 0 PDF CDF Mean Variance E [ T ] = 1 λ Var [ T ] = 1 λ 2 3 Key Property: Memorylessness • Reliability: Amount of time a component has been in service has no effect on the amount of time until it fails • Inter-event times: Amount of time since the last event contains no information about the amount of time until the next event • Service times: Amount of remaining service time is independent of the amount of service time elapsed so far Pr{ T a + b | T b } = Pr{ T a } a , b ≥ Memoryless Property 4 Properties of Exponential Distribution If X 1 and X 2 are independent exponential r.v.’s with parameters (rate) l 1 and l 2 respectively, then P(x1< x2) = l 1/( l 1+ l 2) That is, the probability X1 occurs before X2 is l 1/( l 1+ l 2) Minimum of Two Exponentials: If X 1 , X 2 , …, X n are independent exponential r.v.’s where X n has parameter (rate) l i , then min( X 1 , X 2 , …, X n ) is exponential with parameter (rate) l 1 + l 2 + … + l n Competing Exponentials: 5 Properties of Exponential RV. The probability of 1 event happening in the next ∆ t is Pr{ T ≤ ∆ t ) = 1 - e – λ ∆ t = λ ∆ t When ∆ t is small , (– λ ∆ t )n...
View Full Document

This note was uploaded on 01/06/2011 for the course CHE 6270 taught by Professor Dr.dmitry during the Spring '10 term at University of Florida.

Page1 / 16

Poisson (ISE 484) - 1 Exponential Distribution& Poisson...

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