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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MAE 591 RANDOM DATA Properties: 1. When xt and are uncorrelated , i.e.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/21/2009 for the course ME . taught by Professor . during the Spring '09 term at Korea University.

Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online