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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

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STA107 Lecture 24 Exponential Distribution

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  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

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