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# Lecturenotes12 - STAT 430/510 Lecture 12 STAT 430/510...

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STAT 430/510 Lecture 12 STAT 430/510 Probability Hui Nie Lecture 12 June 17th, 2009

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STAT 430/510 Lecture 12 Review Discussed Uniform Distribution and Normal Distribution Normal Approximation to Binomial Distribution Introduce Exponential Distribution and others.
STAT 430/510 Lecture 12 Exponential Random Variable A continuous random variable X is said to have a exponential distribution with parameter λ if the pdf of X is f ( x ) = ± λ e - λ x , if x 0 0 , if x < 0

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STAT 430/510 Lecture 12 cdf of Exponential r.v. For exponential r.v. X with parameter λ , the cdf is F ( x ) = ± 1 - e - λ x , x 0 0 , x < 0
STAT 430/510 Lecture 12 Expected Value and Variance X is exponential random variable with parameter λ . E [ X ] = 1 λ E [ X 2 ] = 2 λ 2 Var ( X ) = 1 λ 2

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STAT 430/510 Lecture 12 Example Suppose that the length of a phone call in minutes is an exponential random variable with parameter λ = 0 . 1. If someone arrives immediately ahead of you at a public telephone booth, ﬁnd the probability that you will have to wait (a) More than 10 minutes? (b) Between 10 and 20 minutes?
Example: Solution Let X denote the length of the call made by the person in the booth. P

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## This note was uploaded on 06/28/2009 for the course STAT 430 taught by Professor Krieger during the Summer '08 term at UPenn.

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Lecturenotes12 - STAT 430/510 Lecture 12 STAT 430/510...

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