Continuous random variables
This presentation is the property of its rightful owner.
Sponsored Links
1 / 37

Continuous Random Variables PowerPoint PPT Presentation


  • 26 Views
  • Uploaded on
  • Presentation posted in: General

Continuous Random Variables. (most slides borrowed with permission from Andrew Moore of CMU and Google) http://www.cs.cmu.edu/~awm/tutorials. Announcements. CS Welcome event Thursday 3:30, ECCR 265 poster presentations Mozer lab research meeting Wednesdays 11:00-12:30, ECCS 127

Download Presentation

Continuous Random Variables

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Continuous random variables

Continuous Random Variables

(most slides borrowed with permission from Andrew Moore of CMU and Google)

http://www.cs.cmu.edu/~awm/tutorials


Announcements

Announcements

  • CS Welcome event

    • Thursday 3:30, ECCR 265

    • poster presentations

  • Mozer lab research meeting

    • Wednesdays 11:00-12:30, ECCS 127

    • Email me if you’d like to be on our mailing list


Real valued random variables

Real-Valued Random Variables

  • Previous lecture on probability focused on discrete random variables

    • true, false

    • male, female

    • freshman, sophomore, junior, senior

  • Can sometimes quantize real variables to make them discrete

    • E.g., age, height, distance

  • Today: how to handle variables that cannot be quantized


Probability mass vs density

Probability Mass Vs. Density

  • Discreet RVs have a probability mass associated with each value of the variable

    • P(male)=.7, P(female)=.3

  • Imagine if the variablehad an infinitenumber of valuesinstead of a finitenumber…


Probability mass vs density1

Probability Mass Vs. Density

  • Continuous RVs have a probability density associated with each value

    • Probability density function (PDF)

  • Density is derivative of mass

  • Notation: P(…) for mass,p(…) for density


Continuous random variables

= E[X2] - E[X]2


Continuous random variables

Density estimate of automobile

weight and MPG

Note change innotation: Previously

used P(x^y) for

joint


Covariance facts

Covariance Facts

Consider 2D case with (X,Y)

FALSE

TRUE

?

?


Mike s basic advice on continuous random variables

Mike’s Basic Advice on Continuous Random Variables

  • Ignore the fact that p(x) is a probability density function and treat it just as a mass function, and the algebra all works out.

  • Alternatively, turn densities to masses with dx terms, and they should always cancel out.

  • Don’t be freaked when you see a probability density >> 1.

  • Do be freaked if you see a probability mass or density < 0.


  • Login