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Continuous Random Variables: The Uniform Distribution

Connexionsmo dule:m168191 ContinuousRandomVariables:TheUniformDist ribution SusanDeanBarbaraIllowsky, ducedbyTheConnexionsPro jectandlicensedundertheCreativeCommonsAt tributionLicense AbstractThismo duledescrib estheprop ertiesoftheUniformDistributionwhichdescr ib ,inseconds, ,inseconds,followauniformdistributionb etween0and23seconds, ,inseconds,ofaneight-weekoldbaby' U(a,b)wherea=thelowestvalueofXandb= (X) =1b afora X ,X U(0,23)andf(X) =123 0for0 X :Feb20,20097:18pmUS/Central URL: Saylor URL: Attributed to: Barbara Illowsky and Susan Dean Page 1 of 6 Connexionsmo dule:m168192 =a+b2and = (b a)212 Forthisproblem,thetheoreticalmeanandstan darddeviationare =0+232= = (23 0)212= etween2and18seconds?

De nition 2: Uniform Distribution A continuous random ariablev V)(R that has equally likely outcomes over the domain, a<x<b. Often referred as the Rectangular distribution because the graph of the pdf has the form of a rectangle. Notation: X~U (a;b). The mean is = a+b 2 and the standard deviation is ˙= q (ba) 2 12 The probability density ...

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