Continuous Random Variables

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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

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
• 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
• 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. 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

Density estimate of automobile

weight and MPG

Note change innotation: Previously

used P(x^y) for

joint

Covariance Facts

Consider 2D case with (X,Y)

FALSE

TRUE

?

?

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.