Материал: chap2
brs, ɬɚɤ, ɱɬɨɛɵ ars = brs = 0 ɩɪɢ ɫɨɜɩɚɞɟɧɢɢ ɪɚɧɝɨɜ (ɷɬɨ ɟɫɬɟɫɬɜɟɧɧɨ). ȼɫɟɝɨ ɫɨɩɨɫɬɚɜɥɟɧɢɣ
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ɪɚɧɝɨɜ |
t(t 1) |
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¦¦ars2 ɭɦɟɧɶɲɢɬɫɹ ɧɚ |
t(t 1) |
. ȿɫɥɢ ɨɛɴɟɞɢɧɟɧɢɣ |
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ɨɛɴɟɞɢɧɟɧɧɵɯ |
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ɋɭɦɦɚ |
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r s |
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ɧɟɫɤɨɥɶɤɨ, ɫɤɚɠɟɦ, ɪ, ɚtv – ɱɢɫɥɨɨɛɴɟɞɢɧɟɧɧɵɯɪɚɧɝɨɜɜv-ɨɦɨɛɴɟɞɢɧɟɧɢɢɩɨɏ, |
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[114] |
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ɬɨɫɭɦɦɚɭɦɟɧɶɲɢɬɫɹɧɚɜɟɥɢɱɢɧɭ |
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(tv 1) |
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Ux |
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tv |
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v 1 |
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ɉɭɫɬɶ q – ɱɢɫɥɨ ɨɛɴɟɞɢɧɟɧɧɵɯ ɪɚɧɝɨɜ y, ɚ uw – ɱɢɫɥɨ ɨɛɴɟɞɢɧɟɧɧɵɯ ɪɚɧɝɨɜ ɜ w-ɨɦ |
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ɨɛɴɟɞɢɧɟɧɢɢ, ɬɨɝɞɚɫɭɦɦɚ ¦¦brs2 ɭɦɟɧɶɲɢɬɫɹɧɚ |
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q |
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uw (uw 1) |
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U y |
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w 1 |
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ɂɬɚɤ, ɞɥɹɫɥɭɱɚɹɨɛɴɟɞɢɧɟɧɧɵɯɪɚɧɝɨɜɨɤɨɧɱɚɬɟɥɶɧɨɢɦɟɟɦ: |
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P Q |
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. (II,6,5,) |
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N(N 1) |
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N(N 1) |
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ȼ ɨɬɥɢɱɢɟ ɨɬ ȡ ɤɨɷɮɮɢɰɢɟɧɬ IJ ɛɟɡ ɩɨɩɪɚɜɤɢ ɦɟɧɶɲɟ, ɱɟɦ ɤɨɷɮɮɢɰɢɟɧɬ IJ ɫ ɩɨɩɪɚɜɤɨɣ, ɬ.ɟ. ɢɫɩɨɥɶɡɨɜɚɧɢɟ IJ ɛɟɡ ɩɨɩɪɚɜɨɤ ɩɨɜɵɲɚɟɬ ɨɲɢɛɤɭ II ɪɨɞɚ ɢ ɦɟɧɟɟ ɨɩɚɫɧɨ, ɱɟɦ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ȡ ɛɟɡ
ɩɨɩɪɚɜɨɤ(ɫɦ. ɝɥ. V). |
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ɉɪɢɦɟɪ22. Ɋɚɫɫɦɨɬɪɢɦɫɥɟɞɭɸɳɭɸɬɚɛɥɢɰɭ: |
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Ɉɛɴɟɤɬɵ A |
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D |
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H |
K |
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M |
N |
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X |
1,5 |
1,5 |
3 |
4 |
6 |
6 |
6 |
8 |
9,5 |
9,5 |
11 |
12 |
Y |
2,5 |
2,5 |
7 |
4,5 |
1 |
4,5 |
6 |
11,5 |
11,5 |
8,5 |
8,5 |
10 |
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ɑɬɨɩɨɪɨɠɞɚɟɬɜS ɷɥɟɦɟɧɬA? |
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ɉɪɢɫɨɩɨɫɬɚɜɥɟɧɢɢȺɫS, ɨɱɟɜɢɞɧɨ, 0 (ɨɞɢɧɚɤɨɜɵɟɪɚɧɝɢɩɨX), Ⱥɫɋ– ɩɥɸɫɟɞɢɧɢɰɭ(+1) × |
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(+1) = 1, ɚɧɚɥɨɝɢɱɧɨ 1 ɩɨɪɨɠɞɚɟɬɫɨɩɨɫɬɚɜɥɟɧɢɟȺɫ D, F, G, H, K, L, Ɇ, N; ɩɪɢɫɨɩɨɫɬɚɜɥɟɧɢɢȺɫ |
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ȿɩɨɹɜɥɹɟɬɫɹɦɢɧɭɫɟɞɢɧɢɰɚ (ɪɚɧɝɩɨ X ɜɩɪɹɦɨɣ, ɚɩɨ Y – ɜɨɛɪɚɬɧɨɣɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ: 1 × (– |
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1) |
= –1). |
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Ɍɚɤɢɦɨɛɪɚɡɨɦ, ɜɤɥɚɞȺɜ S ɪɚɜɟɧ +8. ɉɪɨɞɨɥɠɚɹɫɨɩɨɫɬɚɜɥɟɧɢɹ, ɩɨɥɭɱɢɦ: S = 8 + 8 + 1 +5 + |
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5 + 5 + 5 – 3 – 2 + 1 + 1 = 34. |
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ȼX – ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢɬɪɢɨɛɴɟɞɢɧɟɧɢɹ: t1 = 2; t2 = 3; t3 = 2; Uɯ = 5; ɜɨɜɬɨɪɨɣ– ɱɟɬɵɪɟ: u1
=u2 = u3 = u4 = 2; Uy = 4. Ɍɟɩɟɪɶɩɨɮɨɪɦɭɥɟ(II,6,5): IJ= 0,55.
ɍɩɪɚɠɧɟɧɢɟ 53. ȼ ɭɩɨɦɢɧɚɜɲɟɣɫɹ ɤɧɢɝɟ «Ɇɟɬɨɞɢɤɚ ɢ ɬɟɯɧɢɤɚ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɨɛɪɚɛɨɬɤɢ ɩɟɪɜɢɱɧɨɣɫɨɰɢɨɥɨɝɢɱɟɫɤɨɣɢɧɮɨɪɦɚɰɢɢ» ɩɪɢɜɨɞɢɬɫɹɬɚɛɥɢɰɚ«ȼɵɱɢɫɥɟɧɢɟ
[115]
ɤɨɷɮɮɢɰɢɟɧɬɚ ɤɨɪɪɟɥɹɰɢɢ ɪɚɧɝɨɜ Ʉɟɧɞɷɥɚ ɦɟɠɞɭ ɨɬɜɟɬɚɦɢ ɪɚɛɨɱɢɯ: «ɢɧɬɟɪɟɫɧɚɹ ɪɚɛɨɬɚ» ɢ «ɨɛɪɚɡɨɜɚɧɢɟɫɨɨɬɜɟɬɫɬɜɭɟɬɪɚɛɨɬɟ» (ɫ. 17). ȼɨɫɩɪɨɢɡɜɟɞɟɦɱɚɫɬɶɟɟ.
Ɋɚɫɫɱɢɬɚɬɶ IJ. ȼ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɨɦɨɱɶ ɜ ɷɬɨɦ ɦɨɠɟɬ ɰɢɬɢɪɭɟɦɚɹ ɤɧɢɝɚ. Ɍɚɦ, ɜ ɱɚɫɬɧɨɫɬɢ, ɩɨɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ
Ɍɚɛɥɢɰɚ28
ɉɪɢɦɟɪɜɵɱɢɫɥɟɧɢɹɤɨɷɮɮɢɰɢɟɧɬɚɪɚɧɝɨɜɨɣɤɨɪɪɟɥɹɰɢɢɄɟɧɞɷɥɚ
ɇɨɦɟɪ |
X –, ɨɬɜɟɬɢɜɲɢɟ, ɱɬɨ |
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ɍ – ɥɢɰɚ, ɨɬɜɟɬɢɜɲɢɟ, ɱɬɨ |
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ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɣ |
ɪɚɧɝɩɨX |
ɨɛɪɚɡɨɜɚɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ |
ɪɚɧɝɩɨɍ |
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ɪɚɛɨɬɚɢɧɬɟɪɟɫɧɚɹ, % |
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ɪɚɛɨɬɟ, % |
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ɝɪɭɩɩɵ |
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79
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100,0 |
3 |
100 |
1 |
2 |
100,0 |
3 |
87,5 |
5,5 |
3 |
100,0 |
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77,0 |
9 |
4 |
100,0 |
3 |
75,0 |
10 |
5 |
100,0 |
3 |
50,0 |
11,5 |
6 |
83,5 |
6,5 |
92,0 |
3 |
7 |
83,5 |
6,5 |
83,5 |
8 |
8 |
83,0 |
8 |
90,0 |
4 |
9 |
82,5 |
9 |
94,5 |
2 |
10 |
71,0 |
10 |
87,0 |
7 |
11 |
55,5 |
11 |
87,5 |
5,5 |
12 |
50,0 |
12 |
50,0 |
11,5 |
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28,5 |
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43,0 |
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14 |
0 |
14 |
0 |
14 |
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Ɋ = 61, Q = 28, ɨɞɧɚɤɨ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ IJ ɧɟ ɭɱɬɟɧɨ, ɱɬɨ ɢɦɟɸɬɫɹ ɨɛɴɟɞɢɧɟɧɢɹ ɪɚɧɝɨɜ. Ⱦɚɠɟ ɟɫɥɢ ȼɵ ɢɫɩɨɥɶɡɭɟɬɟ ɤɧɢɝɭ, ɪɚɫɫɱɢɬɚɣɬɟ IJ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ, ɫ ɭɱɟɬɨɦ ɨɛɴɟɞɢɧɟɧɢɣ. Ⱦɥɹ ɤɨɧɬɪɨɥɹ: Ux = 1, Uy = 2. Ɉɬɜɟɬ: IJ= + 0,39.
ɈɛɨɰɟɧɤɟɫɭɳɟɫɬɜɟɧɧɨɫɬɢIJɜɫɥɭɱɚɟɨɛɴɟɞɢɧɟɧɧɵɯɪɚɧɝɨɜɫɦ. § 8 ɝɥɚɜɵV. Ⱦɨɫɢɯɩɨɪɢɫɩɨɥɶɡɨɜɚɥɢɫɶɮɨɪɦɭɥɵ, ɫɩɪɚɜɟɞɥɢɜɵɟɞɥɹɥɸɛɵɯN, ɨɞɧɚɤɨɭɞɨɛɧɵɟɥɢɲɶɞɥɹ
ɦɚɥɵɯ(ɧɟɛɨɥɟɟ20–30); ɜɩɪɨɬɢɜɧɨɦɫɥɭɱɚɟɜɵɱɢɫɥɟɧɢɹɫɭɳɟɫɬɜɟɧɧɨɡɚɬɪɭɞɧɹɸɬɫɹ.
ɋɟɣɱɚɫ ɦɵ ɪɚɫɫɦɨɬɪɢɦ ɛɨɥɶɲɢɟ N. ȼ ɬɚɤɢɯ ɫɥɭɱɚɹɯ ɩɪɢɡɧɚɤɢ ɲɤɚɥɢɪɭɸɬɫɹ. Ʉɚɤ ɢ ɪɚɧɟɟ,
ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɩɪɢɡɧɚɤ X ɩɪɢɧɢɦɚɟɬ ɡɧɚɱɟɧɢɹ ɯi ɝɞɟ i 1,k , ɚ ɩɪɢɡɧɚɤ Y – ɡɧɚɱɟɧɢɹ yj, ɝɞɟ j 1,l (ɨɛɵɱɧɨ k, l § 5–10). ɗɦɩɢɪɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɫɜɨɞɢɬɫɹ ɜ ɤɨɪɪɟɥɹɰɢɨɧɧɭɸ ɬɚɛɥɢɰɭ ^Nij `,
ɞɥɹɤɨɬɨɪɨɣ ¦¦Nij |
N (ɫɦ. § 1, ɝɥɚɜɵII). |
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[116] |
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ȼɤɚɱɟɫɬɜɟɢɫɯɨɞɧɨɣɜɨɡɶɦɟɦɮɨɪɦɭɥɭ |
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¦¦ars2 , B ¦¦brs2 |
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A B |
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(II,6,6) |
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ɉɪɢ ɛɨɥɶɲɢɯ N ɜɵɩɨɥɧɢɬɶ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ r ɢ s ɨɬ 1 ɞɨ N ɱɪɟɡɜɵɱɚɣɧɨ ɡɚɬɪɭɞɧɢɬɟɥɶɧɨ, ɩɨɷɬɨɦɭɩɟɪɟɣɞɟɦɤɫɭɦɦɢɪɨɜɚɧɢɸɩɨi ɢj ɨɬ1 ɞɨk ɢl ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɋɚɫɫɦɨɬɪɢɦ A. ɇɚɦ ɧɭɠɧɨ ɫɪɚɜɧɢɬɶ ɪɚɧɝɢ ɩɨ X ɤɚɠɞɨɣ ɩɚɪɵ ɨɛɴɟɤɬɨɜ, ɚ ɪɟɡɭɥɶɬɚɬɵ ɩɪɨɫɭɦɦɢɪɨɜɚɬɶ22. Ɉɱɟɜɢɞɧɨ, ɦɨɠɧɨ ɧɟ ɫɪɚɜɧɢɜɚɬɶ ɦɟɠɞɭ ɫɨɛɨɣ ɷɥɟɦɟɧɬɵ ɫɬɪɨɤɢ, ɬɚɤ ɤɚɤ ɭ ɧɢɯ ɨɞɢɧɚɤɨɜɵɟ ɪɚɧɝɢ ɩɨ X. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɫɟ ɷɥɟɦɟɧɬɵ, ɭ ɤɨɬɨɪɵɯ X = ɯ1 (ɜɫɟɝɨ ɢɯ N (x1)), ɦɨɠɧɨ ɧɟ ɫɪɚɜɧɢɜɚɬɶ ɞɪɭɝ ɫ ɞɪɭɝɨɦ, ɧɨ ɫɥɟɞɭɟɬ ɫɪɚɜɧɢɬɶ ɫ ɷɥɟɦɟɧɬɚɦɢ, ɭ ɤɨɬɨɪɵɯ X = ɯ2. Ɍɚɤɨɟ
22 ȼ ɞɚɥɶɧɟɣɲɟɦ ɢɡɥɨɠɟɧɢɢ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɡɧɚɱɟɧɢɹ X ɢ Y ɜɵɩɢɫɚɧɵ ɜ ɬɚɛɥɢɰɟ ɜ ɩɨɪɹɞɤɟ ɜɨɡɪɚɫɬɚɧɢɹ (ɫɜɟɪɯɭ ɜɧɢɡɢɫɥɟɜɚɧɚɩɪɚɜɨ).
80
ɫɪɚɜɧɟɧɢɟ ɩɨɪɨɞɢɬ N (ɯ1) • N (x2) ɟɞɢɧɢɰ, ɚɫɪɚɜɧɟɧɢɟɷɥɟɦɟɧɬɨɜɫ X = ɯ1 ɫɷɥɟɦɟɧɬɚɦɢ, ɭɤɨɬɨɪɵɯ X = x3, ɞɚɟɬN (ɯ1) N (ɯ3) ɟɞɢɧɢɰɢɬ.ɞ. ɉɨɷɬɨɦɭ
A = N(x1) [N(x2) + N(x3) + … +N(xk)] + N(x2) [N(x3) + N(x4) + … +N(xk)] + … + N(xk-1)N(xk) =
AN(x1)>N(x2 ) N(x3 ) ... N(xk )@ N(x2 )>N(x3 ) N(x4 ) ... N(xk )@ ...
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k 1 |
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(II,6,7) |
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N(xk 1)N(xk ) ¦N(xi )¦N(xi p ) |
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ɍɩɪɚɠɧɟɧɢɟ54. ɉɨɤɚɡɚɬɶ, ɱɬɨ |
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l 1 |
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B ¦N(y j )¦N(y j q ) |
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(II,6,8) |
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ɉɟɪɟɣɞɟɦ ɤ ɪɚɫɫɦɨɬɪɟɧɢɸ S. Ɍɟɩɟɪɶ ɞɥɹ ɤɚɠɞɨɣ ɩɚɪɵ ɷɥɟɦɟɧɬɨɜ ɧɭɠɧɨ ɫɪɚɜɧɢɜɚɬɶ ɢ ɪɚɧɝɢ ɩɨX (ars), ɢɪɚɧɝɢɩɨY (brs).
Ɋɚɫɫɦɨɬɪɢɦ ɷɥɟɦɟɧɬɵ ɤɥɟɬɤɢ (i, j). əɫɧɨ, ɱɬɨ ɢɯ ɧɟ ɧɭɠɧɨ ɫɪɚɜɧɢɜɚɬɶ ɧɢ ɫ ɷɥɟɦɟɧɬɚɦɢ i-ɨɣ ɫɬɪɨɤɢ(ɨɛɷɬɨɦɦɵɭɠɟɝɨɜɨɪɢɥɢ), ɧɢɫɷɥɟɦɟɧɬɚɦɢ j-ɝɨɫɬɨɥɛɰɚ(ɭɷɥɟɦɟɧɬɨɜɫɬɨɥɛɰɚɨɞɢɧɚɤɨɜɵɟ ɪɚɧɝɢ ɩɨ Y, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɡɚ ɫɱɟɬ brs ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɫɥɚɝɚɟɦɨɟ ɨɛɪɚɬɢɬɫɹ ɜ ɧɭɥɶ). ɋɬɚɧɟɦ ɫɪɚɜɧɢɜɚɬɶ ɧɟɤɨɬɨɪɵɣ ɷɥɟɦɟɧɬ ɢɡ ɤɥɟɬɤɢ (i, j) ɫ ɷɥɟɦɟɧɬɨɦ ɤɥɟɬɤɢ (i', j'), ɟɫɥɢ i'>i, j'> j. Ɍɚɤɨɟ ɫɪɚɜɧɟɧɢɟ ɞɥɹɤɚɠɞɨɣ ɩɚɪɵɨɛɴɟɤɬɨɜɩɨɪɨɞɢɬ +1 ɜɫɢɥɭɭɩɨɪɹɞɨɱɟɧɧɨɫɬɢ ɩɭɧɤɬɨɜɲɤɚɥɵ (ars = 1, brs = 1). ȿɫɥɢi'>i, ɚj'> j, ɬɨɤɚɠɞɚɹɩɚɪɚɩɨɪɨɞɢɬ–1 (ars = 1, brs = – 1). ɋɭɦɦɢɪɭɹɩɨi',j', ɦɵ
[117]
ɩɟɪɟɛɟɪɟɦ ɜɫɟɜɨɡɦɨɠɧɵɟ ɫɪɚɜɧɟɧɢɹ ɜɵɞɟɥɟɧɧɨɝɨ ɷɥɟɦɟɧɬɚ ɢɡ ɤɥɟɬɤɢ (i, j) ɫɨ ɜɫɟɦɢ ɷɥɟɦɟɧɬɚɦɢ,
k l
ɥɟɠɚɳɢɦɢ ɧɢɠɟ ɢ ɫɩɪɚɜɚ (j'> j, i'>i) ɤɨɬɨɪɵɟ ɞɚɞɭɬ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ¦ ¦Nicjc . ɋɨɩɨɫɬɚɜɥɟɧɢɟ
ic i 1 jc j 1
ɷɥɟɦɟɧɬɚ ɢɡ ɤɥɟɬɤɢ (i,j) ɫ ɷɥɟɦɟɧɬɚɦɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ ɧɢɠɟ ɢ ɫɥɟɜɚ ɨɬ ɷɬɨɣ ɤɥɟɬɤɢ, ɩɨɪɨɠɞɚɟɬ
kj 1
ɫɥɚɝɚɟɦɨɟ ¦¦Nicjc . Ɍɚɤɤɚɤɜɫɟɷɥɟɦɟɧɬɵɤɥɟɬɤɢ(i,j) ɪɚɜɧɨ-
ic i 1 jc 1
Ɍɚɛɥɢɰɚ29
ɋɜɹɡɶɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢɪɚɛɨɬɨɣɫɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɸɫɩɟɰɢɚɥɶɧɨɫɬɶɸ
|
Y |
|
|
|
X |
ɭɞɨɜɥɟɬɜɨɪɟɧ |
ɩɪɨɦɟɠɭɬɨɱɧɚɹ |
ɧɟɭɞɨɜɥɟɬɜɨɪɟɧ |
N(xi) |
|
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ɩɨɡɢɰɢɹ |
|
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ɭɞɨɜɥɟɬɜɨɪɟɧ |
1472 |
50 |
65 |
1587 |
ɩɪɨɦɟɠɭɬɨɱɧɚɹ |
136 |
65 |
42 |
243 |
ɩɨɡɢɰɢɹ |
|
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ɧɟɭɞɨɜɥɟɬɜɨɪɟɧ |
126 |
42 |
165 |
333 |
N(yj) |
1734 |
157 |
272 |
2163 |
ɩɪɚɜɧɵ, ɬɨ ɭɦɧɨɠɚɹ ɪɟɡɭɥɶɬɚɬ ɧɚ NiJ ɢ ɫɭɦɦɢɪɭɹ ɡɚɬɟɦ ɩɨ i ɢ j, ɦɵ ɨɫɭɳɟɫɬɜɢɦ ɜɨɨɛɳɟ ɜɫɟ ɜɨɡɦɨɠɧɵɟɫɪɚɜɧɟɧɢɹɩɚɪɷɥɟɦɟɧɬɨɜ.
ɍɩɪɚɠɧɟɧɢɟ55. ɉɨɱɟɦɭɧɟɧɭɠɧɨɪɚɫɫɦɚɬɪɢɜɚɬɶɫɥɭɱɚɣi'<i? ɂɬɚɤ,
k l k l k j 1
S ¦¦Nij ( ¦ ¦ Nicjc ¦¦Nicjc) (II,6,9)
i 1 j 1 ic i 1 jc j 1 ic i 1 jc 1
ɌɟɦɫɚɦɵɦɦɵɡɚɜɟɪɲɢɥɢɩɟɪɟɯɨɞɤɤɨɪɪɟɥɹɰɢɨɧɧɨɣɬɚɛɥɢɰɟɜɨɜɫɟɯɦɧɨɠɢɬɟɥɹɯIJ23.
Ⱦɥɹ ɢɥɥɸɫɬɪɚɰɢɢ ɷɬɨɣ «ɫɬɪɚɲɧɨɣ» ɮɨɪɦɭɥɵ ɩɪɢɜɟɞɟɦ ɩɪɢɦɟɪ, ɤɨɬɨɪɵɣ ɩɨɤɚɠɟɬ ɫɩɪɚɜɟɞɥɢɜɨɫɬɶɩɨɫɥɨɜɢɰɵ«ɧɟɬɚɤɫɬɪɚɲɟɧɱɟɪɬ, ɤɚɤɟɝɨɪɢɫɭɸɬ».
23 ȺɜɬɨɪɵɜɵɪɚɠɚɸɬɛɥɚɝɨɞɚɪɧɨɫɬɶȽ.ɂ. ɋɚɝɚɧɟɧɤɨɡɚɩɨɦɨɳɶɩɪɢɜɵɜɨɞɟɫɨɨɬɧɨɲɟɧɢɹ(II,6,9).
81
ɉɪɢɦɟɪ 23. ɂɡɭɱɚɹ ɫɜɹɡɶ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢ ɪɚɛɨɬɨɣ (Y) ɫ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɸ ɫɩɟɰɢɚɥɶɧɨɫɬɶɸ(X) ɦɵ, ɜɱɚɫɬɧɨɫɬɢ, ɩɨɥɭɱɢɥɢɤɨɪɪɟɥɹɰɢɨɧɧɭɸɬɚɛɥɢɰɭ29 (ɦɚɫɫɢɜ, ɈɋɊɁ).
[118]
ɌɟɩɟɪɶȺ= 1587 (243 + 333) + 243·333 = 995031; ȼ= 1734 (157 + 272) + 157·272 = 786590;
S = 1472 (65 + 42 + 42 + 165) + 50 (42 + 165 – 136 – 126) – 65 (136 + 65 + 126 + 42) + 136 (42 +
165)+ 65 (165 – 126) – 42 (126 + 42) = 459104;
IJ= +0,52.
Ɍɚɤɢɦɨɛɪɚɡɨɦ, ɦɟɠɞɭɢɡɭɱɚɟɦɵɦɢɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɹɦɢɟɫɬɶɬɟɫɧɚɹɩɨɥɨɠɢɬɟɥɶɧɚɹɫɜɹɡɶ. ɍɩɪɚɠɧɟɧɢɟ 56. Ⱦɥɹ ɩɪɢɡɧɚɤɨɜ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ ɪɚɛɨɬɨɣ (Y), ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ
ɨɛɳɟɫɬɜɟɧɧɨɣɪɚɛɨɬɨɣ(X) ɤɨɪɪɟɥɹɰɢɨɧɧɚɹɬɚɛɥɢɰɚɢɦɟɟɬɜɢɞ:
Ɍɚɛɥɢɰɚ30
ɋɜɹɡɶɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢɪɚɛɨɬɨɣ(Y) ɫɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɸɨɛɳɟɫɬɜɟɧɧɨɣɪɚɛɨɬɨɣ
(X)
|
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Y |
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X |
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N(xi) |
|
Y1 |
Y2 |
Y3 |
||
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|||
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x1 |
1241 |
82 |
150 |
1473 |
|
x2 |
147 |
11 |
38 |
196 |
|
x3 |
103 |
13 |
13 |
129 |
|
|
|
|
|
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|
N(yj) |
1491 |
106 |
201 |
1798 |
|
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|
ȼɵɱɢɫɥɢɬɶIJ. Ɉɬɜɟɬ: IJ= + 0,31.
ɋɜɹɡɶ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɨɠɟ ɩɨɥɨɠɢɬɟɥɶɧɚɹ, ɧɨ ɦɟɧɟɟ ɬɟɫɧɚɹ. ȿɳɟ ɦɟɧɟɟ ɬɟɫɧɨɣ, ɧɚɩɪɢɦɟɪ, ɨɤɚɡɵɜɚɟɬɫɹ ɫɜɹɡɶ ɦɟɠɞɭ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɸ ɪɚɛɨɬɨɣ ɢ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɸ ɞɨɫɭɝɨɦ (ɞɥɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɬɚɛɥɢɰɵ IJ = +0,14), ɱɬɨ ɞɨɩɭɫɤɚɟɬ ɟɫɬɟɫɬɜɟɧɧɭɸ ɢɧɬɟɪɩɪɟɬɚɰɢɸ.
Ʉɨɷɮɮɢɰɢɟɧɬ IJ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɮɨɪɦɭɥɨɣ (II,6,6), ɦɨɠɟɬ ɨɛɪɚɳɚɬɶɫɹ ɜ ±1 ɬɨɥɶɤɨ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚɬɚɛɥɢɰɚɞɢɚɝɨɧɚɥɶɧɚ.
ȼ ɫɚɦɨɦ ɞɟɥɟ, ɫɨɝɥɚɫɧɨ ɧɟɪɚɜɟɧɫɬɜɭ Ʉɨɲɢ24 |S| ɦɚɤɫɢɦɚɥɟɧ, ɟɫɥɢ ɧɚɛɨɪɵ ars ɢ brs ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ: brs = Į · ars. ɗɬɨ ɜɨɡɦɨɠɧɨ ɥɢɲɶ ɬɨɝɞɚ, ɤɨɝɞɚ ɜɫɟ ɧɚɛɥɸɞɟɧɢɹ ɥɢɛɨ ɧɚ ɩɨɥɨɠɢɬɟɥɶɧɨɣ (Į = 1), ɥɢɛɨ ɧɚ ɨɬɪɢɰɚɬɟɥɶɧɨɣ (Į = – 1) ɝɥɚɜɧɨɣ ɞɢɚɝɨɧɚɥɢ ɬɚɛɥɢɰɵ, ɬ.ɟ. ɟɫɥɢ ɬɚɛɥɢɰɚɤɜɚɞɪɚɬɧɚɹ(ɟɫɥɢɟɫɬɶɧɟɞɢɚɝɨɧɚɥɶɧɵɟɷɥɟɦɟɧɬɵ, ɬɨĮɧɟɛɭɞɟɬɡɧɚɤɨ-
[119]
ɩɨɫɬɨɹɧɧɨɣɜɟɥɢɱɢɧɨɣ, ɫɨɨɬɧɨɲɟɧɢɟbrs = Įars ɧɟɛɭɞɟɬɜɵɩɨɥɧɹɬɶɫɹɞɥɹɜɫɟɯɩɚɪɷɥɟɦɟɧɬɨɜ). Ⱦɥɹ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɬɚɛɥɢɰɵ |S| ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɭɦɚ, ɟɫɥɢ: 1) ɜɫɟ ɧɚɛɥɸɞɟɧɢɹ ɥɟɠɚɬ ɜ
ɤɥɟɬɤɚɯ ɫɚɦɨɣ ɞɥɢɧɧɨɣ ɞɢɚɝɨɧɚɥɢ ɬɚɛɥɢɰɵ, ɬ.ɟ. ɞɢɚɝɨɧɚɥɢ, ɫɨɞɟɪɠɚɳɟɣ m = min (k, l) ɤɥɟɬɨɤ, ɬɚɤ ɤɚɤ ɜ ɫɥɭɱɚɟ ɩɨɹɜɥɟɧɢɹ ɧɟɞɢɚɝɨɧɚɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ ɜ S, ɤɪɨɦɟ ɧɭɥɟɣ ɬɢɩɚ 0·0, ɞɨɛɚɜɥɹɸɬɫɹ ɧɭɥɢ ɬɢɩɚars · 0 ɢ0 · brs, ɩɪɢɱɟɦɡɚɫɱɟɬɭɦɟɧɶɲɟɧɢɹɱɢɫɥɚɫɥɚɝɚɟɦɵɯ, ɪɚɜɧɵɯ1;
2) ɜɫɟɧɚɛɥɸɞɟɧɢɹɪɚɜɧɨɦɟɪɧɨɪɚɫɩɪɟɞɟɥɟɧɵɦɟɠɞɭɞɢɚɝɨɧɚɥɶɧɵɦɢɤɥɟɬɤɚɦɢ, ɬ.ɟ. Nii = N/m (ɬɚɤɤɚɤɨɛɵɱɧɨN >> m, ɬɨɦɨɠɧɨɫɱɢɬɚɬɶ, ɱɬɨɨɧɨɤɪɚɬɧɨm ɛɟɡɫɭɳɟɫɬɜɟɧɧɨɣɩɨɬɟɪɢɬɨɱɧɨɫɬɢ).
ɉɪɨɢɥɥɸɫɬɪɢɪɭɟɦɩɟɪɜɨɟɭɬɜɟɪɠɞɟɧɢɟ, ɧɚɩɪɢɦɟɪ, ɞɥɹɫɥɟɞɭɸɳɟɣɬɚɛɥɢɰɵ:
24 Ⱦɥɹɱɢɬɚɬɟɥɹ, ɧɟɡɧɚɤɨɦɨɝɨɫɷɬɢɦɧɟɪɚɜɟɧɫɬɜɨɦ, ɦɵɩɪɢɜɨɞɢɦɟɝɨɜɵɜɨɞɜɤɨɧɰɟɩɚɪɚɝɪɚɮɚ.
82
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X |
Y |
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N(xi) |
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y1 |
y2 |
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x1 |
N11 |
1 |
N11+1 |
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x2 |
0 |
N22 – 1 |
N22 – 1 |
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x3 |
0 |
0 |
0 |
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N(yj) |
N11 |
N22 |
N |
SN11 (N22 1) % N11N22
ɉɪɨɢɥɥɸɫɬɪɢɪɭɟɦ ɜɬɨɪɨɟ ɭɬɜɟɪɠɞɟɧɢɟ. Ɋɚɫɫɦɨɬɪɢɦ, ɧɚɩɪɢɦɟɪ, ɞɢɚɝɨɧɚɥɶɧɭɸ ɬɚɛɥɢɰɭ
3 × 3:
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N(xi) |
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y1 |
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y2 |
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y3 |
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x1 |
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N11 |
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0 |
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0 |
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N11 |
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x2 |
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0 |
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N22 |
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0 |
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N22 |
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x3 |
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0 |
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0 |
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N33 |
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N33 |
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N(yj) |
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N11 |
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N22 |
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N33 |
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N |
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Ⱦɥɹɧɟɟ |
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S N |
11 |
N |
22 |
N |
11 |
N |
33 |
N |
22 |
N |
33 |
d N 2 |
N 2 |
N 2 |
, |
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11 |
22 |
33 |
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Smax |
N 2 /3ɩɪɢN11 |
N22 |
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N33 |
N /3, |
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ɬ.ɟ. [120]
ɟɫɥɢɜɫɟɧɚɛɥɸɞɟɧɢɹɪɚɫɩɪɟɞɟɥɟɧɵɪɚɜɧɨɦɟɪɧɨ. Ɂɞɟɫɶɦɵɢɫɩɨɥɶɡɨɜɚɥɢɢɡɜɟɫɬɧɨɟɧɟɪɚɜɟɧɫɬɜɨ ab bc ac d a2 b2 c2 ,
ɤɨɬɨɪɨɟɥɟɝɤɨɩɨɥɭɱɢɬɶ, ɫɤɥɚɞɵɜɚɹɩɨɱɥɟɧɧɨɬɪɢɨɱɟɜɢɞɧɵɯɧɟɪɚɜɟɧɫɬɜɚ
(a b)2 t 0,(a c)2 t 0,(b c)2 t 0.
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɜ ɤɚɠɞɨɣ ɤɥɟɬɤɟ ɫɚɦɨɣ ɞɥɢɧɧɨɣ ɞɢɚɝɨɧɚɥɢ ɞɨɥɠɧɨ ɛɵɬɶ N/m ɷɥɟɦɟɧɬɨɜ.
ɋɨɩɨɫɬɚɜɥɹɹ ɷɥɟɦɟɧɬɵ ɩɟɪɜɨɣ ɤɥɟɬɤɢ ɫ ɨɫɬɚɥɶɧɵɦɢ, ɦɵ ɩɨɥɭɱɢɦ N N (m 1) ɟɞɢɧɢɰ, ɚ m m
ɷɥɟɦɟɧɬɵ ɜɬɨɪɨɣ ɫ ɩɪɨɱɢɦɢ N N (m 2) , ɬɚɤ ɤɚɤ ɢɯ ɭɠɟ ɧɟ ɧɭɠɧɨ ɫɪɚɜɧɢɜɚɬɶ ɫ ɷɥɟɦɟɧɬɚɦɢ m m
ɩɟɪɜɨɣ ɢ ɬ.ɞ. ȼɢɬɨɝɟ
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ɇɨ ɩɪɢ ɷɬɨɦ ɡɧɚɱɟɧɢɢ S ɤɨɷɮɮɢɰɢɟɧɬ IJ, ɜɨɨɛɳɟ ɝɨɜɨɪɹ, ɧɟ ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɣ ± 1. |
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(II,6,10) |
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Ɉɱɟɜɢɞɧɨ, ɨɧ ɩɪɢɧɢɦɚɟɬ ɡɧɚɱɟɧɢɹ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɞɨɫɬɢɱɶ ± 1 (ɟɫɥɢ ɧɟ ɫɱɢɬɚɬɶ ɧɟɡɧɚɱɢɬɟɥɶɧɨɝɨ ɷɮɮɟɤɬɚ, ɜɨɡɧɢɤɚɸɳɟɝɨ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ N ɧɟ ɤɪɚɬɧɨ ɬ) ɞɚɠɟ ɞɥɹ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɬɚɛɥɢɰ.
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