Transcription of Chapter 3 Continuous Random Variables
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Chapter 3 Continuous Random Variables
Chapter 3 Continuous Random IntroductionRather thansummingprobabilities related to discrete Random Variables , here forcontinuous Random Variables , thedensitycurve isintegratedto determine (Introduction)Patient s number of visits,X, and duration of visit, = value of function,F(3) = P(Y < 3) = 5/12x , pmf f(x)probability (distribution): cdf F(x)probability less than = sum of probabilityat specific valuesP(X < ) = P(X = 0) + P(X = 1)= + = (X = 2) = , pdf f(y) = y/6, 2 < y < 4probability less than 3 = area under curve,P(Y < 3) = 5/12xprobability at 3,P(Y = 3) = 0probability less than = value of functionF( ) = P(X < ) = : Comparing discrete and Continuous distributions7374 Chapter 3.
76 Chapter 3. Continuous Random Variables (LECTURE NOTES 5) with associated standard deviation, ˙= p ˙2. The moment-generating function is M(t) = E 1 etX = Z 1 etXf(x) dx for values of tfor which this integral exists. Expected value, assuming it exists, of a function uof Xis E[u(X)] = Z 1 1 u(x)f(x) dx The (100p)th percentile is a value of ...
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