LEC17 Exponential Dist

LEC17 Exponential Dist - Exponential Distribution...

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Unformatted text preview: Exponential Distribution Exponential r.v. X with rate : pdf: f x e x x ( ) = - cdf: F x e x x ( ) =- - 1 moments: E(X)=1/ V(X)=1/ 2 The Memoryless Property A component has an exponentially distributed lifetime, X, with mean 10 hours. f x e x x ( ) . . = - 1 1 P(X>1)= 1 1 0 90 1 1-- =- ( ) . . ( ) e Given the component has lasted 5000 hours, find the probability the lifetime is at least one more hour. ANS. 0.90 P X X P X X P X P X P X e e e ( / ) ( ) ( ) ( ( [ ] [ ] . . ( ) . ( ) . ( ) = = =---- = =--- 5001 5000 5001 5000 5000 1 1 1 1 90 0 1 5001 0 1 5000 0 1 1 Do you think mechanical parts have an exponential lifetime? 2 The Times Between Events in a Poisson Process are Exponential Arrivals to a queue form a Poisson process with rate is =10 arrivals per second . r.v. N = # arrivals per second Poisson( = 10 ) time P N n e n n n ( ) !...
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LEC17 Exponential Dist - Exponential Distribution...

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