Transcription of Gaussian Probability Density Functions: Properties and ...
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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 <.
second order moments of the pdf, renders its use very common in characterizing the uncertainty in various domains of application. For example, in robotics, it is ... • a two-dimensional vector with the position in a 2D environment, • a three-dimensional vector (2d-position and orientation) representing a mo-
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