Class Notes (836,580)
Canada (509,856)
Mathematics (1,115)
MAT2377 (53)
Lecture 6

Lecture 6 - RandomVariables 3 %28Continuous Models%29.pdf

15 Pages
58 Views
Unlock Document

Department
Mathematics
Course
MAT2377
Professor
Aziz Khanchi
Semester
Fall

Description
MAT23773XSpring20114144ContinuousRandomVariablesDenitionArandomvariableXissaidtobecontinuousifitscumulativedistributionfunctionFisacontinuousfunctionXDenitionLetXbeacontinuousrandomvariablewiththecdfFXTheprobabilitydensityfunctionofXis00FxifFxexistsfx0otherwise0whereFisthederivativeofFNoteWesometimesdenotetheprobabilitydensityfunctionpdfofXasfXExample1ConsideraPoissonprocesswitharateLetXbethelengthoftheintervalrequiredtoobserveachangeinthePoissonprocessShowthatthecdfofXis0x0Fxx1ex0NoteThefunctionFisacontinuousfunction1Propertiesoff1fx0Z1fxdx1213ComputationalPropertyLetARthenZPX2AfxdxAInparticularZxftdtFxPXx1NoteifafunctionfRRsatisestheaboveproperties1and2thenwesaythatfisaprobabilitydensityfunctionOtherpropertiesoff1Asinglevaluedoesnothaveamassieforallx2RPXx02Letab2RsuchthatabthenPaXbPaXbPaXbPaXbZbfxdxFbFaa2
More Less

Related notes for MAT2377

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit