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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

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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
slide19

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.
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