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Continuous Random Variables

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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

Density estimate of automobile

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.