Exponential - Le arning Obje s ctive cognizeand...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Learning Objectives Recognize and use the probability density function of a exponential random variable
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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)
Background image of page 2
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%
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 6
Exercise Exercise #1
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 10

Exponential - Le arning Obje s ctive cognizeand...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online