Lecture23[1]

# Lecture23[1] - Lecture 23 Exponential Distribution Section...

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Exponential Distribution Section 6.4 1 STAT 225, Dallas Bateman, Spring 2010 Lecture 23

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Exponential Distribution An exponential random variable is a continuous random variable that measures the lifetime of some event. The exponential distribution is used to model the behavior of units that have a constant failure rate (or units that do not degrade with time or wear out).
Exponential Distribution Examples : X is the time until the next customer arrives at a grocery store. X is the time until an appliance breaks (lifetime). X is the mileage you get from one tank of gas.

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Exponential Distribution Notation: PDF: CDF: NOTE: If we want to find , then we are finding: ~ ( ) X Exp / ( ) for 0 x e f x x  / ( ) 1 for 0 x F x e x   ) ( x X P / 1 (1 ) x e  x/μ e
Exponential PDF

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Exponential CDF
Exponential Expectation & Variance Expected Value Variance () EX 2 Var X

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Memoryless Property An exponential random variable X has the
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## This note was uploaded on 05/19/2011 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue.

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Lecture23[1] - Lecture 23 Exponential Distribution Section...

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