ContinuousProbability

ContinuousProbability - Notation P(… for mass p(… for...

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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
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Real Numbers 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
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Probability Mass Vs. Density Discreet RVs have a probability  mass  associated with each value of the variable P(male)=.7, P(female)=.3 Continuous RVs have a probability  density   associated with each value Probability density  function Relation between probability mass and  density density = derivative of mass
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Unformatted text preview: Notation: P(…) for mass, p(…) for density • Graph with increasing number of values of variable • Use a binomial = E[X 2 ] - E[X] 2 Density estimate of automobile weight and MPG Covariance Facts Consider 2D case with (X,Y) 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, add the dx terms everywhere, and you’ll see that they 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. Largest possible entropy of any unit-variance distribution...
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ContinuousProbability - Notation P(… for mass p(… for...

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