ch6 - Ch ’u ’ong 6 L ´ Y THUY ´ ˆ ET T ’ U ’ ONG...

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Unformatted text preview: Ch ’u ’ong 6 L ´ Y THUY ´ ˆ ET T ’ U ’ ONG QUAN V ` A H ` AM H ` ˆ OI QUI 1. M ´ ˆ OI QUAN H ˆ E . GI ˜ ’ UA HAI D ¯ A . I L ’ U . ’ ONG NG ˜ ˆ AU NHI ˆ EN Khi kh ’ ao s´at hai ¯ da . i l ’u ’ o . ng ng ˜ ˆau nhiˆ en X, Y ta th ´ ˆay gi ˜ ’ua ch´ung c´o th ’ ˆ e c´o mˆo . t s ´ ˆo quan hˆ e . sau: i) X v`a Y ¯ dˆo . c lˆa . p v ´ ’ oi nhau, t ´ ’uc l`a viˆ e . c nhˆa . n gi´a tri . c’ua ¯ da . i l ’u ’ o . ng ng ˜ ˆau nhiˆ en n`ay khˆong ’ anh h ’u ’ ’ ong ¯ d ´ ˆ en viˆ e . c nhˆa . n gi´a tri . c ’ ua ¯ da . i l ’u ’ o . ng ng ˜ ˆau nhiˆ en kia. ii) X v`a Y c´o m ´ ˆoi phu . thuˆo . c h`am s ´ ˆo Y = ϕ ( X ). iii) X v`a Y c´o s ’u . phu . thuˆo . c t ’u ’ ong quan v`a phu . thuˆo . c khˆong t ’u ’ ong quan. 2. H ˆ E . S ´ ˆ O T ’ U ’ ONG QUAN 2.1 Moment t ’u ’ong quan (Covarian) 2 D ¯ i . nh ngh ˜ ia 1 * Moment t ’ u ’ ong quan (hiˆ e . p ph ’ u ’ ong sai) c ’ ua hai ¯ da . i l ’ u ’ o . ng ng ˜ ˆ au nhiˆ en X v`a Y, k´ ı hiˆ e . u cov ( X,Y ) hay μ XY , l` a s ´ ˆ o ¯ d ’ u ’ o . c x´ ac ¯ di . nh nh ’ u sau cov ( X,Y ) = E { [ X- E ( X )][ Y- E ( Y )] } * N ´ ˆ eu cov ( X,Y ) = 0 th` ı ta n´oi hai ¯ da . i l ’ u ’ o . ng ng ˜ ˆ au nhiˆ en X v`a Y khˆong t ’ u ’ ong quan. Ch´u ´y cov ( X,Y ) = E ( XY )- E ( X ) .E ( Y ) Thˆa . t vˆa . y, ta c´o cov ( XY ) = E { X.Y- X.E ( Y )- Y.E ( X ) + E ( X ) .E ( Y ) = E ( XY )- E ( X ) .E ( Y )- E ( X ) .E ( Y ) + E ( X ) .E ( Y ) = E ( XY )- E ( X ) .E ( Y ) 99 100 Ch ’ u ’ ong 6 . L´y thuy ´ ˆ et t ’u ’ ong quan v` a h` am h ` ˆoi qui ⊕ Nhˆ a . n x´ et 1 * N ´ ˆ eu ( X,Y ) r ` ’ oi ra . c th` ı cov ( X,Y ) = n X i =1 m X j =1 x i y j P ( x i ,y j )- E ( X ) E ( Y ) * N ´ ˆ eu ( X,Y ) liˆ en tu . c th` ı cov ( X,Y ) = + ∞ Z-∞ + ∞ Z-∞ xyf ( x,y ) dxdy- E ( X ) E ( Y ) ⊕ Nhˆ a . n x´ et i) N ´ ˆ eu X v`a Y l`a hai ¯ da . i l ’u ’ o . ng ng ˜ ˆau nhiˆ en ¯ dˆ o . c lˆa . p th` ı ch´ung khˆong t ’u ’ ong quan. ii) Cov(X,X)=Var(X). 2.2 Hˆ e . s ´ ˆo t ’u ’ong quan 2 D ¯ i . nh ngh ˜ ia 2 Hˆ e . s ´ ˆ o t ’ u ’ ong quan c ’ ua hai ¯ da . i l ’ u ’ o . ng ng ˜ ˆ au nhiˆ en X v`a Y, k´ ı hiˆ e . u r XY , l` a s ´ ˆ o ¯ d ’ u ’ o . c x´ac ¯ di . nh nh ’ u sau r XY = cov ( X,Y ) S X .S Y v ´ ’ oi S x ,S Y l` a ¯ dˆ o . lˆ e . ch tiˆ eu chu ’ ˆ an c ’ ua X,Y . • ´ Y ngh ˜ ia c ’ ua hˆ e . s ´ ˆo t ’u ’ ong quan Hˆ e . s ´ ˆo t ’u ’ ong quan ¯ do m ´ ’uc ¯ dˆ o . phu . thuˆo . c tuy ´ ˆ en t´ ınh gi ˜ ’ua X v`a Y . Khi | r XY | c`ang g ` ˆan 1 th` ı m ´ ˆoi quan hˆ e ....
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This note was uploaded on 01/18/2012 for the course INFORMATIK 2011 taught by Professor Phanthuongcang during the Winter '11 term at Cornell.

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ch6 - Ch ’u ’ong 6 L ´ Y THUY ´ ˆ ET T ’ U ’ ONG...

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