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# Continuous Random Variables - PowerPoint PPT Presentation

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

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## PowerPoint Slideshow about 'Continuous Random Variables' - yaakov

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### Continuous Random Variables

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

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

• 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

• 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

• 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…

• 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

= E[X2] - E[X]2

weight and MPG

Note change innotation: Previously

used P(x^y) for

joint

Consider 2D case with (X,Y)

FALSE

TRUE

?

?

• 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.