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CSE 555 -
Gaussian Derivatives
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Gaussian DerivativesIntegral of the Gaussian dxeuerfux∫−=02)/2()(πArea under the standardized GaussianError FunctionGeneralization to any confidence levelnherrorherrorzherrorSSNS))(1)(()(−±• Values of zNfor 2-Sided N% Confidence IntervalsConfidence Level N%:50% 68% 80% 90% 95% 98% 99%Constant zn:0.67 1.00 1.28 1.64 1.96 2.33 2.58Rule of thumb• Binomial is approximated by Normal distribution as long as n >= 30 or when np(1-p) >= 5• For smaller values of n it is wise to use a table giving exact values for the binomial distributionBivariate Normal Densitiesp(X1,X2) Is a hill-shaped surfaceLEVEL CURVES• Slice the surface with horizontal planes which the locus of points with the quadratic formINFORMATION THEORYRelative EntropyMutual
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