Transcription of Gaussian Probability Density Functions: Properties and ...
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Gaussian Probability Density Functions: Properties and ...
Gaussian Probability Density Functions: Properties and Error CharacterizationMaria Isabel RibeiroInstitute for Systems and RoboticsInstituto Superior TcnicoAv. Rovisco Pais, 11049-001 Lisboa M. Isabel Ribeiro, 2004 February 2004 Contents1 Normal random variables22 Normal random for second order .. of constant Probability .. 143 Properties224 Covariance matrices and error ellipsoid241 Chapter 1 Normal random variablesA random variableXis said to be normally distributed with mean and variance 2if its Probability Density function (pdf) isfX(x) =1 2 exp[ (x )22 2], < x < .( )Whenever there is no possible confusion between the random variableXand thereal argument,x, of the pdf this is simply represented byf(x)omitting the explicitreference to the random variableXin the subscript. The Normal or Gaussiandistribution ofXis usually represented by,X N( , 2),or also,X N(x , 2).
Maria Isabel Ribeiro Institute for Systems and Robotics Instituto Superior Tcnico Av. Rovisco Pais, 1 1049-001 Lisboa PORTUGAL {mir@isr.ist.utl.pt} c M. Isabel Ribeiro, 2004 February 2004. Contents 1 Normal random variables 2 2 Normal random vectors 7
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