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Unformatted text preview: 1 Chap. 4: Cont. RV Continuous RV can take on any number an interval. Probability density function (pdf) f ( x ) of a continuous RV X has two key properties: 1. f ( x ) > 0 for all x . 2. . Prob. X is in A = integral of pdf over A Property 2. implies A dx x f A X P ) ( ) ( 1 ) ( dx x f Cumul. Dist. Functions (cdf): F(x) = P(X < x) 0 < F(x) < 1, for all x As As F(x) is nondecreasing. Regions where F is flat are regions of prob. = 0 For a continuous RV, F(x) is a continuous function of x. Wherever the derivative exists, f(x) = dF(x) / dx Same as discrete RV , x ) ( x F 1 ) ( x F , x 3 Expected Values Let X be continuous RV with pdf f . The expected value of X or expectation of X or mean of X , is The expected value of h(X) or is (these integrals must be finite; else, the exp. doesnt exist) Remark: In general, Ex) dx x xf X E X ) ( ] [...
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 Spring '08
 Staff
 Probability

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