Exponential

# Exponential - Le arning Obje s ctive cognizeand...

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Learning Objectives Recognize and use the probability density function of a exponential random variable

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Exponential f X x (29 = λ e x if x 0 0 otherw ise 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 x f(x)
Example Suppose that the time until an mistake is made during a surgical procedure follows an exponential distribution with λ =0.6. What is the probability that a mistake occurs between time units 5 & 6? f X x (29 = λ e x if x 0 0 otherw ise e x dx 5 6 e x 5 6 =- e x 5 6 2%

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Exponential f X x (29 = λ e x if x 0 0 otherw ise lambda E X [ ] = 1 Var X [ ] = 1 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 1 2 3 4 5 6 7 8 9 10 x 0.1 0.2 0.3 0.4 0.5 0.6 More
Example Exponential PDF Exponential CDF ( 29 = - otherwise 0 0 if x e x f x X λ F X x (29 = f X t -∞ x dt F X x = λ e t 0 x F X x =- e t 0 x e x -- F X x ( 29 = 1 - e x 1

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Geometric & Exponential F geo n (29 = 1 - 1 - p ( 29 n F exp x = 1 - e x Exponential is like geometric but with tiny time steps rather than integer “trials” (Refer to pgs 151-152 in B&T) 0 1 2 3 4 5 6 7 8 0 0 .2 0 .4 0 .6 0 .8 1 x CDF exponen tia l geome tric
Exercise Exercise #1

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## This note was uploaded on 02/22/2010 for the course BME 335 taught by Professor Dunn during the Spring '10 term at University of Texas at Austin.

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Exponential - Le arning Obje s ctive cognizeand...

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