1 / 4

STA107 Lecture 24 Exponential Distribution

STA107 Lecture 24 Exponential Distribution . Poisson Distribution X = # of successes in one unit of time; discrete RV l = mean # successes in one unit of time Exponential Distribution T = time between successive successes; continuous RV

cybele
Télécharger la présentation

STA107 Lecture 24 Exponential Distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. STA107 Lecture 24Exponential Distribution Poisson Distribution X = # of successes in one unit of time; discrete RV l = mean # successes in one unit of time Exponential Distribution T = time between successive successes; continuous RV b = 1/l = expected time between successive successes

  2. Cumulative Distribution Function F(t) = P(T ≤ t) = 1- P(T > t) = 1 - P(no successes in the interval (0,t]) = 1- P(X = 0) where X ~ Poisson(tl) = 1 - e-tl Probability Density Function

  3. Mean • E(T) = b = 1/l Variance • Var(T) = b2= 1/l2 Memoryless Property • P(T > b|T> a) = P(T > b-a) b>a

  4. Example Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes,l= 1/10. • What is the probability that a customer will spend more than 15 minutes in the bank? Ans: 0.22 • What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes? Ans: 0.604

More Related