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Gaussian Derivatives
Integral of the Gaussian
dxeuerfu
x
∫−
=0
2
)/2()( π
Area under the standardized Gaussian
Error Function
Generalization to any confidence level
nherrorherrorzherror SS
NS))(1)(()( −
±
• Values of zN for 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 2.58
Rule 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 distribution
Bivariate Normal Densities
p(X1,X2) Is a hill-shaped surface
LEVEL CURVES
• Slice the surface with horizontal planes which the locus of points with the quadratic form
INFORMATION THEORY
Relative Entropy
Mutual Information
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