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ɋɨԙԑɵ ɬɟԙɞɟɭɥɟɪ ɠԛɣɟɫɿ (5.2) ɫɵɡɵԕɬɵԕ ɛɨɥɭ ԛɲɿɧ ɠɭɵԕɬɚɭɲɵ ɮɭɧɤɰɢɹ
Px p0 f0 x p1 f1x ... pn fn x
(5.3)

ɬԛɪɿɧɞɟ ɠɚɡɵɥɭ ɤɟɪɟɤ.

ɮɨɪɦɭɥɚɞɚԑɵ: p0 , p1, ... pn – ɿɲɿɧɞɟ ɿɡɞɟɥɿɩ ɨɬɵɪԑɚɧ ɩɚɪɚɦɟɬɪɥɟɪ ɛɚɪ,

ɬԝɪɚԕɬɵ ɤɨɷɮɮɢɰɢɟɧɬɬɟɪ; f0 x, f1x, ... , fn x – ɚɪɝɭɦɟɧɬɬɿԙ x

ɬԥɭɟɥɫɿɡ ɠԥɧɟ ԛɡɞɿɤɫɿɡ ɫɵɡɵԕɬɵԕ ɮɭɧɤɰɢɹɥɚɪɵ. Ȼԝɥ ɮɭɧɤɰɢɹɥɚɪԑɚ ɛɟɥɝɿɫɿɡ
ɩɚɪɚɦɟɬɪɥɟɪ ɤɿɪɦɟɣɞɿ.
Ɏɭɧɤɰɢɹɧɵԙ (5.3) ɛԝɥ ɬԛɪɿ ɠɚɥɩɵɥɚɧΕɚɧ ɩɨɥɢɧɨɦ ɞɟɩ ɚɬɚɥɚɞɵ, ɚɥ ɨɧɵԙ

ɬԛɣɿɧɞɟɪɞɟɝɿ ɤɨɷɮɮɢɰɢɟɧɬɬɟɪɿɧ ɚɧɵԕɬɚɭɞɵԙ ɫɵɡɵԕɬɵԕ ɬɟԙɞɟɭɥɟɪ ɠԛɣɟɫɿ
p0 f0 xi p1 f1xi ... pn fn xi F xi , i 1, ...k .
(5.4)

Ʉɟɣɛɿɪ ɠɚԑɞɚɣɥɚɪɞɚ, (5.2) ɲɚɪɬɵɧɚ ԕɨɫɚ,

'r xi 0 (5.5)

ɬɟԙɞɟɭɿ ԕɚɧɚԑɚɬɬɚɧɞɵɪɵɥɭ ɤɟɪɟɤ.
Ȼԝɥ ɮɨɪɦɭɥɚɞɚԑɵ 'r xi – ɚɣɵɪɦɚɞɚɧ ' x ɛɨɣɵɧɲɚ ɚɥɵɧԑɚɧ, x xi

ɬɟԙɞɿɝɿɧɟ ɫԥɣɤɟɫ, r ɞԥɪɟɠɟɥɿ ɬɭɵɧɞɵ.

2.2. ɎɭɧɤɰɢɹΕɚ ɤɜɚɞɪɚɬɬɵ ɠɭɵΙɬɚɭ. Ԕɚɪɚɫɬɵɪɵɥԑɚɧ ɬԥɫɿɥɞɿԙ
ɤɟɦɲɿɥɿɝɿ: ɢɧɬɟɪɩɨɥɹɰɢɹɥɚɭ ɬԛɣɿɧɞɟɪɿɧɿԙ ɚɪɚɫɵɧɞɚԑɵ ɛɟɪɿɥɝɟɧ ɮɭɧɤɰɢɹɞɚɧ
ɚɭɵɬԕɭɞɵԙ ɲɚɦɚɫɵ ɛɟɥɝɿɥɿ ɛɿɪ ɦԧɥɲɟɪɞɟɧ ɤԧɩ ɛɨɥɭɵ ɦԛɦɤɿɧ, ԧɣɬɤɟɧɿ (5.2)

ɬɟԙɞɟɭɥɟɪ ɠԛɣɟɫɿɧɞɟ ɛɟɪɿɥɝɟɧ ɮɭɧɤɰɢɹɞɚɧ ɚɭɵɬԕɭɞɵԙ ɲɚɦɚɫɵɧɚ ɟɲԕɚɧɞɚɣ
ɲɟɤɬɟɭ ɲɚɪɬɬɚɪɵ ԕɨɣɵɥɦɚɣɞɵ. Ɉɫɵ ɤɟɦɲɿɥɿɤɬɟɧ, ɮɭɧɤɰɢɹԑɚ ɤɜɚɞɪɚɬɬɵ
ɠɭɵΙɬɚɭ ɬԥɫɿɥɿɧɞɟ ɛɟɥɝɿɥɿ ɛɿɪ ɦԧɥɲɟɪɞɟ ɛɨɥɫɚ ɞɚ ԕԝɬɵɥɭԑɚ ɛɨɥɚɞɵ.
ɋɨɧɵɦɟɧ, ɮɭɧɤɰɢɹԑɚ ɤɜɚɞɪɚɬɬɵ ɠɭɵԕɬɚɭ ɬԥɫɿɥɿ – ɛɟɪɿɥɝɟɧ ɮɭɧɤɰɢɹɞɚɧ
ɨɪɬɚɲɚ ɤɜɚɞɪɚɬɬɵ ɚɭɵɬԕɭɞɵ ɟԙ ɚɡ ɦԧɥɲɟɪɝɟ, ɹԑɧɢ ɦɢɧɢɦɭɦԑɚ ɠɟɬɤɿɡɭɝɟ
ɧɟɝɿɡɞɟɥɝɟɧ. Ⱦɟɦɟɤ,

xm

³ >Px Fx@2 dx
x0 , (5.6)
' ɤɜ
xm x0

ɮɨɪɦɭɥɚɞɚԑɵ x0 , xm – ɚɪɝɭɦɟɧɬɬɿԙ ɠɚԕɵɧɞɚɭ ɤɟɫɿɧɞɿɫɿɧɿԙ ɛɚɫɵɧɞɚԑɵ ɠԥɧɟ

ɫɨԙɵɧɞɚԑɵ ɲɚɦɚɥɚɪɵ.
Ɉɪɬɚɲɚ ɤɜɚɞɪɚɬɬɵ ɚɭɵɬԕɭ ɟԙ ɚɡ (ɦɢɧɢɦɚɥ) ɛɨɥɭ ԛɲɿɧ ɬԧɦɟɧɞɟɝɿ ɢɧɬɟɝɪɚɥ
ɧԧɥɝɟ ɚɣɧɚɥɭ ɤɟɪɟɤ:

xm (5.7)

I ³ >Px Fx@2 dx .
x0

ȿɝɟɪ ɠɚԕɵɧɞɚɭ ɮɭɧɤɰɢɹɫɵɧɞɚ n 1 ɛɟɥɝɿɫɿɡ ɤɨɷɮɮɢɰɢɟɧɬɬɟɪ

( p0 , p1, ..., pn ) ɛɨɥɫɚ, ɨɧɞɚ ɢɧɬɟɝɪɚɥɞɵԙ ɦɢɧɢɦɭɦɵɧ ɚɧɵԕɬɚɭ ԛɲɿɧ

ɢɧɬɟɝɪɚɥɞɵԙ (5.7) ɚɬɚɥԑɚɧ ɤɨɷɮɮɢɰɢɟɧɬɬɟɪ ɚɪԕɵɥɵ ɚɥɵɧԑɚɧ ɞɟɪɛɟɫ
ɬɭɵɧɞɵɥɚɪɵɧ ɧԧɥɝɟ ɬɟԙɟɫɬɿɪɭ ɤɟɪɟɤ, ɹԑɧɢ

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