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09Normal - MAE 591 RANDOM DATA Normal(Gauss Distribution...

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MAE 591 RANDOM DATA Normal (Gauss) Distribution The normal probability density function is expressed by ( ) px x x x x () e x p =− 1 2 2 2 2 πσ µ σ The normal probability distribution function is ( ) Px d x x x x e x p −∞ 1 2 2 2 2 πσ ξµ σ ξ N-dimensional normal distribution: px x x C Cx x C N ij i i j j ij N N (, , , ) exp , 12 1 2 1 2 1 2 2 ⋅⋅⋅⋅⋅ = −− = µµ π where C is the covariance matrix C is the determinant of C C ij is the cofactor of C . ij For N=2, xx x x (, ) exp 12 2 11 1 2 12 1 22 2 2 2 1 2 2 1 21 2 = + ρ µ σ ρ µ σ µ σ µ σ πσ σ ρ where the normalized covariance or correlation coefficient ( )( ) [ ] ρ σσ 12 112 2 = Ex x 1
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MAE 591 RANDOM DATA Properties: 1. When xt and are uncorrelated , i.e.
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09Normal - MAE 591 RANDOM DATA Normal(Gauss Distribution...

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