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ch4 - Chuong 4 ^ D U'OC LU'ONG THAM SO CUA AI LU'ONG ~ ^ ^...

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Ch ’u ’ong 4 U ´ OC L U . ONG THAM S ´ ˆ O C UA D ¯ A . I L U . ONG NG ˜ ˆ AU NHI ˆ EN Gi a s ’u ¯ da . i l ’u ’ o . ng ng ˜ ˆau nhiˆ en X c´o tham s ´ ˆo θ ch ’ua bi ´ ˆ et. U ´ oc l ’u ’ o . ng tham s ´ ˆo θ l`a d ’u . a v`ao m ˜ ˆau ng ˜ ˆau nhiˆ en W x = ( X 1 , X 2 , . . . , X n ) ta ¯ d ’ua ra th ´ ˆong kˆ e ˆ θ = ˆ θ ( X 1 , X 2 , . . . , X n ) ¯ d ˆ e ’u ´ oc l ’u ’ o . ng (d ’u . ¯ do´ an) θ . C´o 2 ph ’u ’ ong ph´ap ’u ´ oc l ’u ’ o . ng: i) U ´ oc l ’u ’ o . ng ¯ di ˆ em: ch i ra θ = θ 0 n`ao ¯ o ¯ d ˆ e ’u ´ oc l ’u ’ o . ng θ . ii) U ´ oc l ’u ’ o . ng kho ang: ch i ra mˆo . t kho ang ( θ 1 , θ 2 ) ch ´ ’ua θ sao cho P ( θ 1 < θ < θ 2 ) = 1 - α cho tr ’u ´ oc (1 - α go . i l`a ¯ dˆo . tin cˆa . y c’ua ’u ´ oc l ’u ’ o . ng). 1. C ´ AC PH U ONG PH ´ AP U ´ OC L U . ONG D ¯ I ˆ EM 1.1 Ph ’u ’ong ph´ ap h` am ’u ´ ’oc l ’u ’o . ng Mˆo t a ph ’u ’ ong ph´ ap Gi’a s ’u c ` ˆan ’u ´ oc l ’u ’ o . ng tham s ´ ˆo θ c’ua ¯ da . i l ’u ’ o . ng ng ˜ ˆau nhiˆ en X. T ` ’u X ta lˆa . p m ˜ ˆau ng ˜ ˆau nhiˆ en W X = ( X 1 , X 2 , . . . , X n ). Cho . n th ´ ˆong kˆ e ˆ θ = ˆ θ ( X 1 , X 2 , . . . , X n ). Ta go . i ˆ θ l`a h` am ’ u ´ oc l ’ u ’ o . ng c ua X . Th ’u . c hiˆ e . n ph´ ep th ’u ta ¯ d ’u ’ o . c m ˜ ˆau cu . th ˆ e w x = ( x 1 , x 2 , . . . , x n ). Khi ¯ d´o ’u ´ oc l ’u ’ o . ng ¯ di ˆ em c ua θ l`a gi´a tri . θ 0 = ˆ θ ( x 1 , x 2 , . . . , x n ). a) U ´ oc l ’u ’ o . ng khˆong chˆ e . ch 2 D ¯ i . nh ngh ˜ ia 1 Th ´ ˆ ong kˆ e ˆ θ = ˆ θ ( X 1 , X 2 , . . . , X n ) ¯ d ’ u ’ o . c go . i l`a ’ u ´ oc l ’ u ’ o . ng khˆong chˆ e . ch c ua tham s ´ ˆ o θ n ´ ˆ eu E ( ˆ θ ) = θ . ´ Y ngh ˜ ia Gi a s ’u ˆ θ l`a ’u ´ oc l ’u ’ o . ng khˆong chˆ e . ch c ua tham s ´ ˆo θ . Ta c´o E ( ˆ θ - θ ) = E ( ˆ θ ) - E ( θ ) = θ - θ = 0 69
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70 Ch ’ u ’ ong 4 . U ´ oc l ’u ’ ong tham s ´ ˆo c’ua ¯ da . i l ’u ’ ong ng ˜ ˆ au nhiˆ en Vˆa . u ’u ´ oc l ’u ’ o . ng khˆong chˆ e . ch l`a ’u ´ oc l ’u ’ o . ng c´o sai s ´ ˆo trung b` ınh b ` ˘ ang 0. Nhˆ a . n x´ et i) Trung b` ınh c ua m ˜ ˆau ng ˜ ˆau nhiˆ en X l`a ’u ´ oc l ’u ’ o . ng khˆong chˆ e . ch c ua trung b` ınh c ua t ˆong th ˆ e θ = E ( X ) = m v` ı E ( X ) = m . ii) Ph ’u ’ ong sai ¯ di ` ˆ eu ch inh c ua m ˜ ˆau ng ˜ ˆau nhiˆ en S 0 2 l`a ’u ´ oc l ’u ’ o . ng khˆong chˆ e . ch c ua ph ’u ’ ong sai c’ua t ˆong th ˆ e σ 2 v` ı E ( S 0 2 ) = σ 2 . ı du . 1 Chi ` ˆ eu cao c ua 50 cˆay lim ¯ d ’ u ’ o .
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