Gaussian Derivatives

Integral of the Gaussian

dxeuerfu

x

∫−

=0

2

)/2()( π

Area under the standardized Gaussian

Error Function

Generalization to any confidence level

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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