Transcription of The Gaussian distribution
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The Gaussian distribution
4 3 2 = 0, = 1 = 1, =1/2 = 0, = 2 Figure 1: Examples of univariate GaussianpdfsN(x; , 2).The Gaussian distributionProbably the most-important distribution in all of statistics is theGaussian distribution ,also calledthenormal Gaussian distribution arises in many contexts and is widely used formodeling continuous random probability density function of the univariate (one-dimensional) Gaussian distribution isp(x| , 2) =N(x; , 2) =1 Zexp( (x )22 2).The normalization constantZisZ= 2 parameters and 2specify the mean and variance of the distribution , respectively: =E[x]; 2= var[x].Figure 1 plots the probability density function for several sets of parameters( , 2).
the normal distribution. The Gaussian distribution arises in many contexts and is widely used for ... The d-dimensional multivariate Gaussian distribution is speci˙ed by the parameters and . Without any further restrictions, specifying requires dparameters and specifying requires a
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