Davydov
.pdf
ɢɧɬɟɪɜɚɥɨɜ ɢ ɜɵɱɢɫɥɢɦ ɟɟ ɡɧɚɱɟɧɢɟ. ɉɨɥɭɱɚɟɦ
k = max { min { = 0=94406. 10
3. Ⱥɧɚɥɨɝɢɱɧɨ ɪɚɡɞɟɥɭ 4 ɩɪɢɦɟɪɚ ɪɚɛɨɬɵ 1 ɧɚɣɞɟɦ ɱɚɫɬɨɬɵ z1>. . . >z10, ɝɞɟ zn ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɦɟɧɬɨɜ ɜɵɛɨɪɤɢ, ɩɪɢɧɚɞɥɟɠɚ- ɳɢɯ ɱɚɫɬɢɱɧɨɦɭ ɢɧɬɟɪɜɚɥɭ Ln. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ d ɥɟɜɵɣ ɤɨɧɟɰ ɢɧɬɟɪɜɚɥɚ [min {; max {] ɢ ɨɩɪɟɞɟɥɢɦ ɟɝɨ ɜ ɫɪɟɞɟ SWP: d = min {. ɉɨɥɭɱɚɟɦ ɜɟɤɬɨɪ ɱɚɫɬɨɬ z = (1>5>8>9>18>14>10>5>7>4). ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Ghilqlwlrqv + Qhz Ghilqlwlrq ɨɩɪɟɞɟɥɢɦ ɟɝɨ ɜ ɫɪɟɞɟ SWP.
4. ɋ ɭɪɨɜɧɟɦ ɡɧɚɱɢɦɨɫɬɢ = 0=05 ɩɪɨɜɟɪɢɦ ɧɭɥɟɜɭɸ ɝɢɩɨɬɟɡɭ K0: ɝɟɧɟɪɚɥɶɧɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶ [ ɪɚɫɩɪɟɞɟɥɟɧɚ ɩɨ ɧɨɪɦɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɩɪɨɬɢɜ ɤɨɧɤɭɪɢɪɭɸɳɟɣ ɝɢɩɨɬɟɡɵ K1: ɧɟ K0. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɤɪɢɬɟɪɢɟɦ ɩɪɨɜɟɪɤɢ ɹɜɥɹɟɬɫɹ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ
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ɝɞɟ zn ɱɚɫɬɨɬɵ, sn ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɞɚɧɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢ- ɧɵ [ ɧɚ ɢɧɬɟɪɜɚɥ Ln, p ɱɢɫɥɨ ɢɧɬɟɪɜɚɥɨɜ (p = 10). ȿɫɥɢ ɜɟɪɧɚ ɝɢɩɨɬɟɡɚ K0, ɬɨ "2 ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ ɉɢɪɫɨɧɚ ɫ = p u 1 ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ, ɝɞɟ u ɪɚɜɧɨ ɱɢɫɥɭ ɩɚɪɚɦɟɬɪɨɜ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ [, ɡɚɦɟɧɟɧɧɵɯ ɧɚ ɢɯ ɨɰɟɧɤɢ ɩɪɢ ɩɨɞɫɱɟɬɟ ɜɟɪɨɹɬɧɨɫɬɟɣ sn (ɭ ɧɚɫ u = 2, ɬɚɤ ɤɚɤ ɩɪɢɦɟɧɹɸɬɫɹ ɨɰɟɧɤɢ = 5=6859 ɢ
= 2=0848). ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Ghilqlwlrqv + Qhz Ghilqlwlrq
ɨɩɪɟɞɟɥɢɦ q = 81, ɢ ɜ ɫɪɟɞɟ SWP. ɂɡɜɟɫɬɧɨ ɬɚɤɠɟ, ɱɬɨ
Pr([ 5 [d>e]) = NormalDist(e> > ) NormalDist(d> > ).
ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɜɵɱɢɫɥɹɟɦ ɧɚɛɥɸɞɚɟɦɨɟ ɡɧɚɱɟ-
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q = 6=7517.
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ɇɚɯɨɞɢɦ ɤɪɢɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ "2ɤɪɢɬ , ɤɨɬɨɪɨɟ ɪɚɡɞɟ- ɥɹɟɬ ɨɛɥɚɫɬɶ ɩɪɢɧɹɬɢɹ ɧɭɥɟɜɨɣ ɝɢɩɨɬɟɡɵ K0 ɢ ɤɪɢɬɢɱɟɫɤɭɸ ɨɛɥɚɫɬɶ. ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɩɨɥɭɱɚɟɦ ɤɪɢɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
"2ɤɪɢɬ =
ChiSquareInv(1 >p u 1) = ChiSquareInv(0=95>7) = 14=067.
Ɍɚɤ ɤɚɤ "2ɧɚɛɥ = 6=7517 ? "2ɤɪɢɬ = 14=067, ɬɨ ɝɢɩɨɬɟɡɚ K0 ɩɪɢɧɢɦɚɟɬɫɹ. Ʌɭɱɲɟ ɫɤɚɡɚɬɶ, ɱɬɨ ɞɚɧɧɵɟ ɧɚɛɥɸɞɟɧɢɣ (ɜɵɛɨɪɤɚ) ɧɟ
ɩɪɨɬɢɜɨɪɟɱɚɬ ɬɨɦɭ, ɱɬɨ ɝɟɧɟɪɚɥɶɧɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶ [ ɩɨɞɱɢɧɹɟɬɫɹ ɧɨɪɦɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɫ ɩɚɪɚɦɟɬɪɚɦɢ = 5=6859 ɢ = 2=0848.
7.Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ 4. ɋɪɚɜɧɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɣ
1)ɋɨɫɬɚɜɢɬɶ ɜɵɛɨɪɤɭ ɨɛɴɟɦɨɦ q{ = 91 + P (P = Q mod 4 + Q mod 3, Q ɧɨɦɟɪ ɫɬɭɞɟɧɬɚ ɩɨ ɫɩɢɫɤɭ ɝɪɭɩɩɵ) ɢɡ ɧɨɪɦɚɥɶ- ɧɨɣ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ [ ɫ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ ɨɠɢɞɚ-
ɧɢɟɦ { = 812 ɢ ɫɪɟɞɧɢɦ ɤɜɚɞɪɚɬɢɱɟɫɤɢɦ ɨɬɤɥɨɧɟɧɢɟɦ { = 13 ɢ ɜɵɛɨɪɤɭ ɨɛɴɟɦɨɦ q| = q{ 2 ɢɡ ɧɨɪɦɚɥɶɧɨɣ ɝɟɧɟɪɚɥɶ-
ɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ \ ɫ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ ɨɠɢɞɚɧɢɟɦ | = 812+P mod 3 ɢ ɫɪɟɞɧɢɦ ɤɜɚɞɪɚɬɢɱɟɫɤɢɦ ɨɬɤɥɨɧɟɧɢɟɦ | = 13=2.
2)ɇɚɣɬɢ ɨɰɟɧɤɢ {¯, |¯, v{ɢ v|.
3)ɉɨ ɩɨɥɭɱɟɧɧɵɦ ɜɵɛɨɪɤɚɦ ɫ ɩɨɦɨɳɶɸ ɬɟɫɬɚ Ɏɢɲɟɪɚ ɋɧɟ- ɞɟɤɨɪɚ ɩɪɢ ɭɪɨɜɧɟ ɡɧɚɱɢɦɨɫɬɢ = 0=05 ɩɪɨɜɟɪɢɬɶ ɝɢɩɨɬɟɡɭ
ɨ ɬɨɦ, ɱɬɨ ɞɢɫɩɟɪɫɢɢ 2{ ɢ 2| ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ [ ɢ \ ɪɚɜɧɵ.
4)ɉɨ ɩɨɥɭɱɟɧɧɵɦ ɜɵɛɨɪɤɚɦ ɫ ɩɨɦɨɳɶɸ ɬɟɫɬɚ ɋɬɶɸɞɟɧɬɚ ɩɪɢ ɭɪɨɜɧɟ ɡɧɚɱɢɦɨɫɬɢ = 0=05 ɩɪɨɜɟɪɢɬɶ ɝɢɩɨɬɟɡɭ ɨ ɬɨɦ, ɱɬɨ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɨɠɢɞɚɧɢɹ { ɢ | ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫ-
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ɬɟɣ [ ɢ \ ɪɚɜɧɵ, ɩɪɟɞɩɨɥɚɝɚɹ, ɱɬɨ ɢɯ ɞɢɫɩɟɪɫɢɢ 2{ ɢ 2| ɪɚɜɧɵ, ɧɨ ɧɟ ɢɡɜɟɫɬɧɵ.
8.ɉɪɢɦɟɪ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ 4
1.ɉɭɫɬɶ q{ = 10, q{ = 9> { = 827, | = 823> { = 12 ɢ
| = 12=2. Ⱥɧɚɥɨɝɢɱɧɨ ɪɚɡɞɟɥɭ 1 ɩɪɢɦɟɪɚ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ 1
ɩɨɫɬɪɨɢɦ ɧɭɠɧɵɟ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɜɵɛɨɪɤɢ.
[: 841=11>820=24>829=82>809=69>814=05>826=74>795=98>821=68> 814=96>826=67=
\: 841=62>815=62>825=0>830=97>816=40>849=05>825=25>815=48> 817=53.
2. Ⱥɧɚɥɨɝɢɱɧɨ ɪɚɡɞɟɥɭ 2 ɩɪɢɦɟɪɚ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ 1 ɧɚɯɨɞɢɦ ɨɰɟɧɤɢ ɩɚɪɚɦɟɬɪɨɜ { ɢ { ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ [. ɉɨɥɭɱɚ-
ɟɦ: Mean(s): 820=09, Standard deviation(s): 12=378, ɬ.ɟ. {¯ = 820=09 ɢ v{ = 12=378. ɋ ɩɨɦɨɳɶɸ ɩɢɤɬɨɝɪɚɦɦɵ Qhz Ghilqlwlrq ɨɩɪɟɞɟ- ɥɢɦ ɡɧɚɱɟɧɢɹ {¯ ɢ v{ɜ ɫɪɟɞɟ SWP.
Ⱦɥɹ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ \ ɩɨɥɭɱɚɟɦ Mean(s): 826=32, Standard deviation(s): 12=160, ɬ.ɟ |¯ = 826=32 ɢ v| = 12=160. ɋ
ɩɨɦɨɳɶɸ ɩɢɤɬɨɝɪɚɦɦɵ Qhz Ghilqlwlrq ɨɩɪɟɞɟɥɢɦ ɡɧɚɱɟɧɢɹ |¯ ɢ v|ɜ ɫɪɟɞɟ SWP.
ɇɚɩɨɦɧɢɦ, ɱɬɨ ɨɰɟɧɤɢ ɩɨɞɫɱɢɬɵɜɚɥɢɫɶ ɩɨ ɮɨɪɦɭɥɚɦ
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3.ɋɧɚɱɚɥɚ ɩɪɨɜɟɪɢɦ ɝɢɩɨɬɟɡɭ ɨ ɪɚɜɟɧɫɬɜɟ ɞɢɫɩɟɪɫɢɣ ɭ [ ɢ \
ɫɩɨɦɨɳɶɸ ɬɟɫɬɚ Ɏɢɲɟɪɚ ɋɧɟɞɟɤɨɪɚ ɢ, ɟɫɥɢ ɷɬɨ ɩɨɞɬɜɟɪɞɢɬɫɹ, ɬɨ ɩɪɨɜɟɪɢɦ ɝɢɩɨɬɟɡɭ ɨ ɪɚɜɟɧɫɬɜɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɨɠɢɞɚɧɢɣ ɭ [
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ɢ \ , ɢɫɩɨɥɶɡɭɹ ɬɟɫɬ ɋɬɶɸɞɟɧɬɚ, ɤɨɬɨɪɵɣ ɬɪɟɛɭɟɬ, ɱɬɨɛɵ ɞɢɫɩɟɪɫɢɢ ɛɵɥɢ ɪɚɜɧɵ, ɯɨɬɹ ɢɯ ɡɧɚɱɟɧɢɹ ɧɟ ɢɡɜɟɫɬɧɵ.
Ɉɫɧɨɜɧɚɹ (ɧɭɥɟɜɚɹ) ɝɢɩɨɬɟɡɚ K0: 2{ = 2| ɩɪɨɬɢɜ ɤɨɧɤɭɪɢɪɭɸ- ɳɟɣ ɝɢɩɨɬɟɡɵ K1: 2{ A 2|. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɤɪɢɬɟɪɢɟɦ ɬɟɫɬɚ ɹɜɥɹɟɬɫɹ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ
I = v2{ A 1, v2|
ɤɨɬɨɪɚɹ ɪɚɫɩɪɟɞɟɥɟɧɚ ɩɨ ɡɚɤɨɧɭ Ɏɢɲɟɪɚ ɋɧɟɞɟɤɨɪɚ ɫɨ ɫɬɟɩɟɧɹɦɢ
ɫɜɨɛɨɞɵ 1 = q{ 1 = 9 ɢ 2 = q| 1 = 8 (ɟɫɥɢ ɜɟɪɧɚ ɧɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ).
ɇɚɣɞɟɦ ɧɚɛɥɸɞɚɟɦɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ Iɧɚɛɥ = v2{@v2| = 1=0362. ɇɚɯɨɞɢɦ ɤɪɢɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ Iɤɪɢɬ, ɤɨɬɨɪɨɟ ɪɚɡɞɟɥɹɟɬ ɨɛɥɚɫɬɶ ɩɪɢɧɹɬɢɹ ɧɭɥɟɜɨɣ ɝɢɩɨɬɟɡɵ ɢ ɤɪɢɬɢɱɟɫɤɭɸ ɨɛɥɚɫɬɶ. ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɧɚɯɨɞɢɦ
Iɤɪɢɬ = FInv(1 > 1> 2) = FInv(0=95>9>8) = 3=3881.
Ɍɚɤ ɤɚɤ Iɧɚɛɥ ? Iɤɪɢɬ, ɬɨ ɩɪɢɧɢɦɚɟɬɫɹ ɧɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ ɨ ɪɚɜɟɧɫɬɜɟ ɞɢɫɩɟɪɫɢɣ ɭ [ ɢ \ , ɬ.ɟ. ɞɚɧɧɵɟ ɧɚɛɥɸɞɟɧɢɣ ɧɟ ɩɪɨɬɢɜɨɪɟɱɚɬ ɬɨɦɭ, ɱɬɨ ɝɟɧɟɪɚɥɶɧɵɟ ɫɨɜɨɤɭɩɧɨɫɬɢ [ ɢ \ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɵɟ ɞɢɫɩɟɪɫɢɢ.
4.ɉɪɨɜɟɪɢɦ ɝɢɩɨɬɟɡɭ ɨ ɪɚɜɟɧɫɬɜɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɨɠɢɞɚɧɢɣ
ɭ[ ɢ \ ɫ ɩɨɦɨɳɶɸ ɬɟɫɬɚ ɋɬɶɸɞɟɧɬɚ.
Ɉɫɧɨɜɧɚɹ (ɧɭɥɟɜɚɹ) ɝɢɩɨɬɟɡɚ K00 : { = | ɩɪɨɬɢɜ ɤɨɧɤɭɪɢɪɭɸ- |
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ɤɨɬɨɪɚɹ ɪɚɫɩɪɟɞɟɥɟɧɚ ɩɨ ɡɚɤɨɧɭ ɋɬɶɸɞɟɧɬɚ ɫɨ ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ= q{ + q| 2 = 17 (ɟɫɥɢ ɜɟɪɧɚ ɧɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ). ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɩɨɥɭɱɚɟɦ
14
v0 = s |
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+ 8v2 |
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Ɍɨɝɞɚ ɧɚɛɥɸɞɚɟɦɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ
Wɧɚɛɥ = W = |
{¯ |¯ |
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12=276q |
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ɇɚɯɨɞɢɦ ɤɪɢɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ Wɤɪɢɬ, ɤɨɬɨɪɨɟ ɪɚɡɞɟɥɹɟɬ ɨɛɥɚɫɬɶ ɩɪɢɧɹɬɢɹ ɧɭɥɟɜɨɣ ɝɢɩɨɬɟɡɵ ɢ ɤɪɢɬɢɱɟɫɤɭɸ ɨɛɥɚɫɬɶ (ɩɪɢ K10 ɤɪɢɬɢ- ɱɟɫɤɚɹ ɨɛɥɚɫɬɶ ɞɜɭɫɬɨɪɨɧɧɹɹ). ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɧɚ-
ɯɨɞɢɦ Wɤɪɢɬ = TInv(1 @2> ) = TInv(0=975>17) = 2=1098. Ɍɚɤ ɤɚɤ |Wɧɚɛɥ| ? Wɤɪɢɬ, ɬɨ ɩɪɢɧɢɦɚɟɬɫɹ ɧɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ ɨ ɪɚɜɟɧɫɬɜɟ
ɫɪɟɞɧɢɯ ɭ [ ɢ \ , ɬ.ɟ. ɞɚɧɧɵɟ ɧɚɛɥɸɞɟɧɢɣ ɧɟ ɩɪɨɬɢɜɨɪɟɱɚɬ ɬɨɦɭ, ɱɬɨ ɝɟɧɟɪɚɥɶɧɵɟ ɫɨɜɨɤɭɩɧɨɫɬɢ [ ɢ \ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɵɟ ɦɚɬɟɦɚɬɢ- ɱɟɫɤɢɟ ɨɠɢɞɚɧɢɹ.
9.Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ 5. Ⱦɢɫɩɟɪɫɢɨɧɧɵɣ ɚɧɚɥɢɡ
1) ɋɨɫɬɚɜɢɬɶ p = 5 ɜɵɛɨɪɨɤ ɨɛɴɟɦɨɦ q = 6 + Q mod 4 + Q mod 3 (Q ɧɨɦɟɪ ɫɬɭɞɟɧɬɚ ɩɨ ɫɩɢɫɤɭ ɝɪɭɩɩɵ) ɢɡ ɧɨɪɦɚɥɶ- ɧɵɯ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ [1>. . . >[p ɫ ɦɚɬɟɦɚɬɢɱɟ- ɫɤɢɦɢ ɨɠɢɞɚɧɢɹɦɢ l = 9 + 0=1q + 0=01l( 1)l, l = 1>p, ɢ ɫɪɟɞɧɢɦɢ ɤɜɚɞɪɚɬɢɱɟɫɤɢɦɢ ɨɬɤɥɨɧɟɧɢɹɦɢ = 3.
2)ɋ ɩɨɦɨɳɶɸ ɬɟɫɬɚ Ʉɨɱɪɚɧɚ ɩɪɢ ɭɪɨɜɧɟ ɡɧɚɱɢɦɨɫɬɢ = 0=05 ɩɪɨɜɟɪɢɬɶ ɝɢɩɨɬɟɡɭ ɨ ɬɨɦ, ɱɬɨ ɝɟɧɟɪɚɥɶɧɵɟ ɫɨɜɨɤɭɩɧɨɫɬɢ [1>. . . >[p ɢɦɟɸɬ ɪɚɜɧɵɟ ɞɢɫɩɟɪɫɢɢ, ɬ.ɟ. 21 =. . . = 2p.
3)ɋ ɩɨɦɨɳɶɸ ɬɟɫɬɚ Ɏɢɲɟɪɚ ɩɪɢ ɭɪɨɜɧɟ ɡɧɚɱɢɦɨɫɬɢ = 0=05
ɩɪɨɜɟɪɢɬɶ ɝɢɩɨɬɟɡɭ ɨ ɬɨɦ, ɱɬɨ ɝɟɧɟɪɚɥɶɧɵɟ ɫɨɜɨɤɭɩɧɨɫɬɢ [1>. . . >[p ɢɦɟɸɬ ɪɚɜɧɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɨɠɢɞɚɧɢɹ, ɬ.ɟ.
1 =. . . = p.
15
10. ɉɪɢɦɟɪ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ 5
1. ɉɭɫɬɶ p = 5, q = 7, l = 8 + 0=01l( 1)l, l = 1>5, ɢ = 2. ɉɪɢɦɟɧɹɹ ɤɨɦɚɧɞɭ Vwdwlvwlfv + Udqgrp Qxpehuv, ɨɬɤɪɨɟɦ
ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ, ɜ ɤɨɬɨɪɨɦ ɜɵɛɟɪɟɦ Qrupdo ɜ ɩɨɥɟ Glvwulexwlrq, ɧɚɛɟɪɟɦ 7 ɜ ɩɨɥɟ Krz Pdq|?, 7=99 ɜ ɩɨɥɟ Phdq, 2 ɜ ɩɨɥɟ Vwdqgdug Ghyldwlrq ɢ ɡɚɤɪɨɟɦ ɨɤɧɨ (RN). ɉɨɥɭɱɚɟɦ ɜɵɛɨɪɤɭ ɨɛɴɟɦɨɦ q = 7. ɉɨɫɬɚɜɢɦ ɤɪɚɫɧɭɸ ɡɚɩɹɬɭɸ ɩɨɫɥɟ ɩɨɫɥɟɞɧɟɝɨ ɱɥɟɧɚ ɩɨɥɭɱɟɧɧɨɣ ɜɵɛɨɪɤɢ ɢ ɩɨɜɬɨɪɢɦ ɩɪɟɞɵɞɭɳɭɸ ɨɩɟɪɚɰɢɸ ɟɳɟ 4 ɪɚɡɚ, ɤɚɠɞɵɣ ɪɚɡ ɧɚɛɢɪɚɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɞɥɹ
Phdq: 2 = 8=02, 3 = 7=97, 4 = 8=04, 5 = 7=95. ɉɨɥɭɱɢɥɢ 35
ɱɢɫɟɥ, ɪɚɡɞɟɥɟɧɧɵɯ ɡɚɩɹɬɵɦɢ.
7=7779>10=765>5=9956>6=0270>7=5724>12=619>4=4621>9=4495> 8=8663>11=905>3=6167>6=203>10=113>7=2038>10=768>7=654 9>4=638 3> 10=96>5=3231>9=062 4>9=5369>9=3381>9=1626>9=3143>7=7863>8=5062> 11=763>6=5013>6=3847>6=6862>8=8231>7=9903>7=3341>11=413>5=519.
ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Pdwulfhv + Uhvkdsh ɨɬɤɪɵɜɚɟɦ ɞɢɚɥɨɝɨ- ɜɨɟ ɨɤɧɨ, ɜ ɤɨɬɨɪɨɦ ɧɚɛɢɪɚɟɦ 7 ɤɚɤ Qxpehu ri Froxpqv ɢ ɡɚɤɪɵ- ɜɚɟɦ ɨɤɧɨ. ɉɨɥɭɱɢɥɢ 5×7-ɦɚɬɪɢɰɭ, ɫɬɪɨɤɚɦɢ ɤɨɬɨɪɨɣ ɹɜɥɹɸɬɫɹ 5 ɜɵɛɨɪɨɤ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɢɡ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ [1,. . . ,[5. ȼɵɞɟɥɢɦ (ɡɚɤɪɚɫɢɦ) ɦɚɬɪɢɰɭ ɢ ɫ ɩɨɦɨɳɶɸ ɩɢɤɬɨɝɪɚɦɦɵ Eudfnhwv ɜɨɡɶɦɟɦ ɟɟ ɜ ɤɜɚɞɪɚɬɧɵɟ ɫɤɨɛɤɢ, ɩɟɪɟɞ ɤɨɬɨɪɵɦɢ ɧɚɛɟɪɟɦ ɜ ɦɚɬɟ- ɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟ (ɤɪɚɫɧɵɦ) { =. ɉɨɥɭɱɢɦ
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5 |
7=7779 |
10=765 |
5=9956 |
6=0270 |
7=5724 |
12=619 |
4=4621 |
6 |
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9=4495 |
8=8663 |
11=905 |
3=6167 |
6=203 |
10=113 |
7=2038 |
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{ = |
9 |
10=768 |
7=6549 |
4=6383 |
10=96 |
5=3231 |
9=0624 |
9=5369 |
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79=3381 9=1626 9=3143 7=7863 8=5062 11=763 6=5013 8 6=3847 6=6862 8=8231 7=9903 7=3341 11=413 5=519
Ɂɚɤɥɸɱɢɦ ɩɨɥɭɱɟɧɧɵɟ ɱɢɫɥɚ ɜ ɫɤɨɛɤɢ, ɩɨɫɬɚɜɢɦ ɩɟɪɟɞ ɧɢɦɢ { = ɢ ɨ ɩ ɪ ɟ ɞ ɟ ɥ ɢ ɦ ɩɨɥɭɱɟɧɧɭɸ ɦɚɬɪɢɰɭ ɜ ɫɪɟɞɟ SWP, ɢɫɩɨɥɶɡɭɹ ɤɨɦɚɧɞɭ Ghilqlwlrqv + Qhz Ghilqlwlrq. ɂɬɚɤ, ɧɟɨɛɯɨ- ɞɢɦɵɟ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɧɚɛɥɸɞɟɧɢɹ {lm (l = 1>5, m = 1>7) ɩɨɥɭɱɟɧɵ
16
ɢɨɩɪɟɞɟɥɟɧɵ ɜ ɫɪɟɞɟ SWP.
2.ɋ ɭɪɨɜɧɟɦ ɡɧɚɱɢɦɨɫɬɢ = 0=05 ɩɪɨɜɟɪɢɦ ɧɭɥɟɜɭɸ ɝɢɩɨɬɟɡɭ
K0: ɞɢɫɩɟɪɫɢɢ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ [1>. . . >[5 ɪɚɜɧɵ (ɬ.ɟ.
21 =. . . = 25) ɩɪɨɬɢɜ ɤɨɧɤɭɪɢɪɭɸɳɟɣ ɝɢɩɨɬɟɡɵ K1: ɧɟ K0. ɂɡɜɟɫɬ- ɧɨ, ɱɬɨ ɤɪɢɬɟɪɢɟɦ ɩɪɨɜɟɪɤɢ ɹɜɥɹɟɬɫɹ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ
v2
F = pmax ,
X
v2n
n=1
ɝɞɟ v2n ɢɫɩɪɚɜɥɟɧɧɚɹ ɨɰɟɧɤɚ ɞɢɫɩɟɪɫɢɢ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ [n. ȿɫɥɢ ɜɟɪɧɚ ɝɢɩɨɬɟɡɚ K0, ɬɨ F ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ Ʉɨɱɪɚɧɚ ɫ 1 = q 1 ɢ 2 = p ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ.
Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɨɰɟɧɨɤ vn ɢ {¯n (ɨɧɢ ɩɨɬɪɟɛɭɸɬɫɹ ɩɪɢ ɜɵɩɨɥɧɟ-
ɧɢɢ ɪɚɡɞɟɥɚ 3) ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Pdwulfhv + Wudqvsrvh ɬɪɚɧɫɩɨ- ɧɢɪɭɟɦ1 ɦɚɬɪɢɰɭ {. ɉɪɢɦɟɧɢɦ ɤ ɬɪɚɧɫɩɨɧɢɪɨɜɚɧɧɨɣ ɦɚɬɪɢɰɟ ɤɨ- ɦɚɧɞɭ Vwdwlvwlfv + Phdq, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɨɰɟɧɤɢ {¯1,. . . ,{¯5, ɝɞɟ
{¯l = 1 Pq {¯l>m, ɩɨɫɥɟ ɱɟɝɨ ɫɧɨɜɚ ɩɪɢɦɟɧɢɦ ɷɬɭ ɤɨɦɚɧɞɭ ɤ ɩɨɥɭɱɟɧ-
q m=1
ɧɵɦ ɨɰɟɧɤɚɦ, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɨɰɟɧɤɭ {¯ = 1 Pp
p l=1
Ɍɟɩɟɪɶ ɧɚɣɞɟɦ ɨɰɟɧɤɢ vn. ɉɨɫɬɚɜɢɦ ɬɟɤɫɬɨɜɨɣ ɤɭɪɫɨɪ ɜ ɩɨɥɟ ɬɪɚɧɫɩɨɧɢɪɨɜɚɧɧɨɣ ɦɚɬɪɢɰɵ ɢ ɩɪɢɦɟɧɢɦ ɤɨɦɚɧɞɭ Vwdwlvwlfv + Vwdqgdug Ghyldwlrq. Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ.
5 |
7=7779 |
9=449 5 |
10=768 |
9=3381 |
6=3847 |
6 |
10=765 |
8=8663 |
7=654 9 |
9=162 6 |
6=6862 |
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9 |
5=9956 |
11=905 |
4=6383 |
9=3143 |
8=8231 |
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6=027 |
3=6167 |
10=96 |
7=786 3 |
7=9903 |
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9 |
7=5724 |
6=203 |
5=3231 |
8=5062 |
7=3341 |
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9 |
12=619 |
10=113 |
9=0624 |
11=763 |
11=413 |
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9 |
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9 |
4=462 1 |
7=203 8 |
9=536 9 |
6=501 3 |
5=519 |
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1ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɜ ɦɚɬɪɢɰɟ SWP ɪɚɫɫɦɚɬɪɢɜɚɟɬ ɜɵɛɨɪɤɢ (ɜɟɤɬɨɪɵ) ɩɨ ɫɬɨɥɛɰɚɦ.
17
Standard deviation(s): [2=8738>2=7501>2=5153>1=6216>1=9481], Mean(s): [7=8884>8=1939>8=2777>8=9103>7=7358], Mean(s): 8=2012.
ɉɟɪɟɞ ɜɟɤɬɨɪɨɦ ɫ vn ɧɚɛɢɪɚɟɦ (ɤɪɚɫɧɵɦ) v =, ɩɟɪɟɞ ɜɟɤɬɨɪɨɦ ɫ {¯n ɧɚɛɢɪɚɟɦ2 | =, ɩɟɪɟɞ {¯ ɧɚɛɢɪɚɟɦ } ɢ ɫ ɩɨɦɨɳɶɸ Qhz Ghilqlwlrq ɨɩɪɟɞɟɥɹɟɦ v, | ɢ } ɜ ɫɪɟɞɟ SWP. ɉɨɥɭɱɚɟɦ
v = [2=8738>2=7501>2=5153>1=6216>1=9481];
| = [7=8884>8=1939>8=2777>8=9103>7=7358] ; } = 8=2012.
ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɜɵɱɢɫɥɹɟɦ ɧɚɛɥɸɞɚɟɦɨɟ ɡɧɚɱɟ- ɧɢɟ ɤɪɢɬɟɪɢɹ. ɉɨɥɭɱɚɟɦ
F |
= |
max2 v |
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ɇɚɯɨɞɢɦ ɤɪɢɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ Fɤɪɢɬ, ɤɨɬɨɪɨɟ ɪɚɡɞɟ- ɥɹɟɬ ɨɛɥɚɫɬɶ ɩɪɢɧɹɬɢɹ ɧɭɥɟɜɨɣ ɝɢɩɨɬɟɡɵ K0 ɢ ɤɪɢɬɢɱɟɫɤɭɸ ɨɛɥɚɫɬɶ. Ʉ ɫɨɠɚɥɟɧɢɸ, ɜ SWP ɧɟɬ ɧɟ ɬɨɥɶɤɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɮɭɧɤɰɢɣ ɞɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ʉɨɱɪɚɧɚ, ɧɨ ɜ Khos ɧɟɬ ɢ ɬɚɛɥɢɰ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɤɪɢɬɢɱɟɫɤɢɯ ɡɧɚɱɟɧɢɣ ɞɥɹ ɷɬɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɉɨɷɬɨɦɭ ɩɪɢɯɨ- ɞɢɬɫɹ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɭɱɟɛɧɢɤɚɦɢ ɢɥɢ ɡɚɞɚɱɧɢɤɚɦɢ, ɜ ɤɨɬɨɪɵɯ ɢɦɟɸɬɫɹ ɬɚɤɢɟ ɬɚɛɥɢɰɵ. ɋɭɳɟɫɬɜɭɟɬ ɢ ɞɪɭɝɨɣ ɫɩɨɫɨɛ ɞɨɩɨɥɧɢɬɶ Khos, ɩɨɦɟɫɬɢɜ ɬɚɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɚɛɥɢɰɵ3 (ɢ ɧɟ ɬɨɥɶɤɨ ɞɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ʉɨɱɪɚɧɚ). ɂɬɚɤ, ɢɡ ɬɚɛɥɢɰɵ Ʉɨɱɪɚɧɚ ɞɥɹ ɭɪɨɜɧɹ ɡɧɚɱɢɦɨɫɬɢ = 0=05 ɢ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ 1 = q 1 = 6, 2 =
p = 5 ɧɚɯɨɞɢɦ Fɤɪɢɬ = 0=5063.
Ɍɚɤ ɤɚɤ Fɧɚɛɥ = 0=28904 ? Fɤɪɢɬ = 0=5063, ɬɨ ɝɢɩɨɬɟɡɚ K0 ɜɟɪɧɚ. Ʌɭɱɲɟ ɫɤɚɡɚɬɶ, ɱɬɨ ɞɚɧɧɵɟ ɧɚɛɥɸɞɟɧɢɣ ɧɟ ɩɪɨɬɢɜɨɪɟɱɚɬ
ɬɨɦɭ, ɱɬɨ ɞɢɫɩɟɪɫɢɢ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ [1>. . . >[5 ɪɚɜɧɵ
(ɬ.ɟ. 21 =. . . = 25).
2ȼ SWP {¯ ɨɡɧɚɱɚɟɬ ɫɨɩɪɹɠɟɧɧɨɟ ɤɨɦɩɥɟɤɫɧɨɟ ɱɢɫɥɨ. ɉɨɷɬɨɦɭ ɜɦɟɫɬɨ {¯ ɭɩɨɬɪɟɛɥɹɟɦ |.
3ȼ ɪɚɡɞɟɥɟ 15 ɦɨɠɧɨ ɧɚɣɬɢ ɢɧɫɬɪɭɤɰɢɢ ɩɨ ɜɫɬɪɚɢɜɚɧɢɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɮɚɣɥɨɜ ɫ ɩɪɢɦɟɧɟɧɢɟɦ Windows-ɬɟɯɧɨɥɨɝɢɢ ɩɨɢɫɤɚ.
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3. ɋ ɭɪɨɜɧɟɦ ɡɧɚɱɢɦɨɫɬɢ = 0=05 ɩɪɨɜɟɪɢɦ ɧɭɥɟɜɭɸ ɝɢɩɨɬɟɡɭ K00 : ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɨɠɢɞɚɧɢɹ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ ɪɚɜɧɵ (ɬ.ɟ. 1 =. . . = 5) ɩɪɨɬɢɜ ɤɨɧɤɭɪɢɪɭɸɳɟɣ ɝɢɩɨɬɟɡɵ K10 : ɧɟ K00 . ɂɡɜɟɫɬɧɨ, ɱɬɨ ɩɪɢ ɭɫɥɨɜɢɢ ɪɚɜɟɧɫɬɜɚ ɞɢɫɩɟɪɫɢɣ ɤɪɢɬɟɪɢɟɦ ɩɪɨɜɟɪ- ɤɢ ɹɜɥɹɟɬɫɹ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ
I = |
Gɮɚɤɬ@(p 1) |
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Gɨɫɬɚɬ@(pq p) |
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p q |
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ɝɞɟ Gɮɚɤɬ = q (¯{l {¯)2 ɢ Gɨɫɬɚɬ = |
({l>m {¯l)2. ȿɫɥɢ ɜɟɪɧɚ |
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l=1 m=1 |
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ɝɢɩɨɬɟɡɚ K00 , ɬɨ I ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ Ɏɢɲɟɪɚ ɫ 1 = p 1 = 4
ɢ2 = pq p = 30 ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ.
ɋɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɜɵɱɢɫɥɹɟɦ ɧɚɛɥɸɞɚɟɦɨɟ ɡɧɚɱɟ- ɧɢɟ ɤɪɢɬɟɪɢɹ. ɂɫɩɨɥɶɡɭɹ ɜɜɟɞɟɧɧɵɟ ɪɚɧɟɟ ɨɛɨɡɧɚɱɟɧɢɹ ɞɥɹ ɨɰɟɧɨɤ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɨɠɢɞɚɧɢɣ {¯l = |l ɢ {¯ = }, ɩɨɥɭɱɚɟɦ
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5 |
(|l })2 |
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30 · 7 |
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=1 |
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Iɧɚɛɥ = |
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lP |
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= 0=25208.4 |
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7 |
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lP P |
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4 |
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({l>m |l)2 |
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=1 m=1
ɇɚɯɨɞɢɦ ɤɪɢɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ Iɤɪɢɬ , ɤɨɬɨɪɨɟ ɪɚɡɞɟ- ɥɹɟɬ ɨɛɥɚɫɬɶ ɩɪɢɧɹɬɢɹ ɧɭɥɟɜɨɣ ɝɢɩɨɬɟɡɵ K00 ɢ ɤɪɢɬɢɱɟɫɤɭɸ ɨɛɥɚɫɬɶ. ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɩɨɥɭɱɚɟɦ
Iɤɪɢɬ = FInv(1 >p 1>pq p) = FInv(0=95>4>30) = 2=6896.
Ɍɚɤ ɤɚɤ Iɧɚɛɥ = 0=25208 ? Iɤɪɢɬ = 2=6896, ɬɨ ɝɢɩɨɬɟɡɚ K00 ɩɪɢɧɢɦɚɟɬɫɹ, ɬ.ɟ. ɞɚɧɧɵɟ ɧɚɛɥɸɞɟɧɢɣ (ɜɵɛɨɪɤɢ) ɧɟ ɩɪɨɬɢɜɨɪɟɱɚɬ
ɬɨɦɭ, ɱɬɨ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɨɠɢɞɚɧɢɹ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ
[1>. . . >[5 ɪɚɜɧɵ (ɬ.ɟ. 1 =. . . = 5).
4Ɉɛɪɚɳɚɟɦ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ, ɱɬɨ ɢɧɞɟɤɫɵ ɭ ɷɥɟɦɟɧɬɨɜ {l>m ɦɚɬɪɢɰɵ ɞɨɥɠɧɵ ɛɵɬɶ ɪɚɡɞɟɥɟɧɵ ɡɚɩɹɬɨɣ.
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11.Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ 6. Ⱥɩɩɪɨɤɫɢɦɚɰɢɹ ɮɭɧɤɰɢɣ
1)ɇɚɣɬɢ ɪɟɲɟɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ
|00 + q{|0 + | = q{(cos { + 1) + {,
ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɟ ɧɚɱɚɥɶɧɵɦ ɭɫɥɨɜɢɹɦ |(0) = 0, |0(0) = 2, ɫ ɩɨɦɨɳɶɸ ɩɪɢɛɥɢɠɟɧɧɵɯ ɦɟɬɨɞɨɜ, ɝɞɟ q = Q (Q ɧɨɦɟɪ ɫɬɭɞɟɧɬɚ ɩɨ ɫɩɢɫɤɭ ɝɪɭɩɩɵ). Ɂɚɬɚɛɭɥɢɪɨɜɚɬɶ ɡɧɚɱɟɧɢɹ ɪɟɲɟɧɢɹ |({) ɧɚ ɢɧɬɟɪɜɚɥɟ [0; 1] ɫ ɲɚɝɨɦ 0.1.
2)ɉɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤ ɪɟɲɟɧɢɹ |({) ɧɚ ɢɧɬɟɪɜɚɥɟ [0; 5].
3)ȼɡɹɜ 5 ɬɨɱɟɤ ɫ ɚɛɫɰɢɫɫɚɦɢ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ 0, 2, 3, 4, 5 ɧɚ ɝɪɚɮɢɤɟ ɪɟɲɟɧɢɹ |({), ɧɚɣɬɢ ɩɨ ɷɬɢɦ ɬɨɱɤɚɦ ɢɧɬɟɪɩɨɥɹɰɢ- ɨɧɧɵɣ ɦɧɨɝɨɱɥɟɧ i({) ɫɬɟɩɟɧɢ 4 ɢ ɩɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤɢ ɮɭɧɤ- ɰɢɢ i({) + 0=1 ɢ ɪɟɲɟɧɢɹ |({) ɧɚ ɨɞɧɨɦ ɪɢɫɭɧɤɟ.
4) ȼɡɹɜ 6 ɬɨɱɟɤ ɫ ɚɛɫɰɢɫɫɚɦɢ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ 0, 1, 2, 3, 4, 5 ɧɚ ɝɪɚɮɢɤɟ ɪɟɲɟɧɢɹ |({), ɧɚɣɬɢ ɩɨ ɷɬɢɦ ɬɨɱɤɚɦ ɥɢɧɢɸ ɪɟɝɪɟɫɫɢɢ | ɧɚ { ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ. ɉɨɫɬɪɨɢɬɶ
ɟɟɝɪɚɮɢɤ ɢ ɜɵɛɪɚɧɧɵɟ ɬɨɱɤɢ ɧɚ ɨɬɞɟɥɶɧɨɦ ɪɢɫɭɧɤɟ.
12.ɉɪɢɦɟɪ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ 6
ȿɫɥɢ ɞɚɧɚ ɮɭɧɤɰɢɹ i({) ɢ ɬɨɱɤɢ Pn ({n>i({n)), n = 0>1>. . . >q, ɧɚ ɟɟ ɝɪɚɮɢɤɟ, ɬɨ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɦ ɦɧɨɝɨɱɥɟɧɨɦ
Sq({) = dq{q + === + d1{ + d0
ɹɜɥɹɟɬɫɹ ɚɥɝɟɛɪɚɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɫɬɟɩɟɧɢ q ɬɚɤɨɣ, ɱɬɨ i({n) =
Sq({n) ɞɥɹ ɜɫɟɯ n = 0>q.
Ʌɢɧɢɟɣ ɪɟɝɪɟɫɫɢɢ | ɧɚ {, ɩɨɫɬɪɨɟɧɧɨɣ ɧɚ ɛɚɡɟ ɬɨɱɟɤ Pn ɦɟɬɨ- ɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ, ɹɜɥɹɟɬɫɹ ɩɪɹɦɚɹ, ɡɚɞɚɧɧɚɹ ɭɪɚɜɧɟɧɢɟɦ
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