ТОПИН.Лекции, задания / variant
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Найти выборочные коэффициенты корреляции Спирмена и Кендалла.
Решение.
Составим последовательности рангов по убыванию баллов на каждом экзамене:
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Вычислим di: d1 = 1 – 5 = -4; d2 = 2 – 1 = 1; d3 = 3 – 2 = 1; d4 = 4 – 4 = 0; |
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d5 = 5 – 3 = 2; d6 = 6 – 8 = -2; d7 = 7 – 7 = 0; d8 = 8 – 6 = 2; d9 = d10 = 0. |
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Найдем |
ådi2 |
= 16 + 1 + 1 + 4 + 4 + 4 = 30. |
Тогда выборочный коэффициент |
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ранговой корреляции Спирмена |
ρB = 1 - |
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6 × 30 |
= 0,818. |
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1000 -10 |
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Приступим к вычислению коэффициента корреляции Кендалла. Определим, сколько рангов, больших данного, располагается справа от каждого yi:
R1 = 5; R2 = 8; R3 = 7; R4 = 5; R5 = 5; R6 = 2; R7 = 2; R8 = 2; R9 = 1; R10 = 0; R = 5 + 8 + 7 + 5 + 5 + 2 + 2 + 2 + 1 = 37; τ В = 104 × 37× 9 -1 = 0,644.
Заметим, что величины выборочных коэффициентов корреляции позволяют предполагать существование связи между результатами экзаменов. Для
проверки этого предположения следует проверить гипотезу о значимости соответствующего выборочного коэффициента ранговой корреляции.
Задания для курсовой работы включают по 6 задач. В них требуется выполнить следующие действия:
Задача 1. По данным выборки
1)построить статистический ряд распределения;
2)изобразить гистограмму;
3)вычислить выборочное среднее;
4)вычислить выборочную дисперсию.
Задача 2. Используя метод наименьших квадратов, найти параметры зависимости y = f(ax + b) :
а) в предположении, что эта зависимость линейна;
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б) в предположении, что зависимость нелинейна, выбрав по форме данных
еенаиболее вероятный вид. В ответе требуется указать:
1)коэффициенты a и b для линейной зависимости;
2)форму нелинейной зависимости;
3)коэффициенты a и b для нелинейной зависимости;
4)величины средних квадратических отклонений для линейного и нелиней- ного случая.
Задача 3. По данным выборки, удовлетворяющей нормальному закону распределения, вычислить:
1)выборочное среднее;
2)исправленное выборочное среднее квадратическое отклонение;
3)доверительный интервал для математического ожидания при доверитель- ной вероятности γ;
4)доверительный интервал для среднего квадратического отклонения для того же значения γ.
Задача 4. По данным выборки, удовлетворяющей нормальному закону распределения со средним квадратическим отклонением s , вычислить
1)выборочное среднее;
2)доверительный интервал для математического ожидания при доверительной вероятности γ.
Задача 5. По данным выборки двумерной случайной величины определить:
1)вектор математического ожидания;
2)вектор дисперсии;
3)выборочный коэффициент корреляции;
4)выборочное уравнение прямой линии регрессии Y на X в виде Y = aX + b.
Задача 6. По данным двух выборок вычислить коэффициенты ранговой корреляции Спирмена и Кендалла.
Примечание 1.
Ответы на курсовые задания имеются у авторов данного методического пособия и могут быть предоставлены преподавателям, использующим его в работе со студентами.
Примечание 2.
Для выдачи большего количества различных вариантов заданий преподава- тели могут воспользоваться программой «TASKMAKER», содержащей все задания, приведенные в пособии, практически в неограниченном количестве вариантов.
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ВАРИАНТЫ КУРСОВЫХ ЗАДАНИЙ
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Вариант №1 |
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Задача 1. |
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2.0 |
4.8 |
5.2 |
3.8 |
3.5 |
3.2 |
3.2 |
3.9 |
4.9 |
2.8 |
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3.7 |
1.8 |
3.4 |
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2.3 |
3.2 |
4.5 |
0.5 |
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3.3 |
2.8 |
2.5 |
1.4 |
3.2 |
3.5 |
2.2 |
2.3 |
3.5 |
3.5 |
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4.1 |
4.4 |
2.3 |
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1.9 |
2.2 |
3.8 |
3.4 |
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2.2 |
3.1 |
2.1 |
2.1 |
3.2 |
2.5 |
2.1 |
2.9 |
2.8 |
3.1 |
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4.3 |
2.8 |
4.0 |
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2.3 |
2.7 |
2.4 |
2.4 |
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2.3 |
2.4 |
2.9 |
2.2 |
3.6 |
2.1 |
3.2 |
2.3 |
2.9 |
2.0 |
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4.7 |
3.5 |
2.8 |
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3.0 |
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3.1 |
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3.3 |
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2.6 |
2.6 |
1.8 |
4.3 |
1.8 |
0.7 |
4.6 |
3.0 |
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1.9 |
3.7 |
3.2 |
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2.6 |
4.2 |
2.9 |
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2.3 |
5.4 |
3.3 |
3.1 |
2.8 |
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2.7 |
2.7 |
1.8 |
2.8 |
4.6 |
2.7 |
1.4 |
3.9 |
3.7 |
2.5 |
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Задача 2. |
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8.0 |
9.0 |
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16.9 |
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24.5 |
31.0 |
35.2 |
41.3 |
48.2 |
57.0 |
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64.6 |
72.3 |
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Задача 3.
γ = 0.95 18.3 15.5 24.5 24.7 18.0 13.3 15.4 10.1 23.1 19.3 5.7 11.6 14.3 -4.5 20.3 32.3
Задача 4. |
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s = 9, γ = 0.99 |
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38.3 |
26.1 |
10.5 |
26.9 |
25.4 |
12.1 |
12.3 |
15.1 |
14.0 |
21.6 |
23.5 |
13.0 |
21.4 |
24.1 |
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26.6 |
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25.8 |
12.7 |
15.2 |
32.9 |
22.1 |
25.7 |
13.6 |
27.8 |
22.8 |
10.1 |
27.8 |
23.8 |
19.8 |
24.7 |
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29.2 |
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24.4 |
5.6 |
19.4 |
30.1 |
15.3 |
8.4 |
14.2 |
22.8 |
30.8 |
36.2 |
22.0 |
20.5 |
14.1 |
18.6 |
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14.7 |
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24.1 |
26.9 |
26.2 |
8.8 |
22.5 |
26.3 |
37.0 |
37.3 |
25.1 |
17.4 |
37.1 |
29.6 |
27.9 |
30.1 |
6.2 |
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20.8 |
27.0 |
19.2 |
20.9 |
28.0 |
22.2 |
12.7 |
15.5 |
19.6 |
24.5 |
24.2 |
35.4 |
34.7 |
25.1 |
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19.6 |
40.8 |
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30.1 |
26.1 |
43.0 |
40.3 |
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25.0 |
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8.1 |
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28.4 |
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Задача 5. |
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( 41.2, 116.5) (48.1, 124.6) ( 53.2, 153.9) ( 39.1, |
99.0) ( 50.2, 191.6) |
( 39.0, |
94.9) |
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( 39.4, 100.2) ( 50.2, 178.6) ( 48.3, 118.7) ( 39.6, 117.0) ( 41.3, |
81.7) |
( 35.2, |
88.0) |
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( 47.9, 159.4) ( 34.6, 124.4) ( 33.2, 103.4) (35.7, |
94.9) |
( 36.8, |
90.8) ( 50.8, 180.5) |
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( 44.5, 152.0) ( 46.3, 167.6) ( 34.8, 84.6) ( 39.2, 124.5) ( 36.8, 131.7) |
( 46.0, |
99.8) |
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( 40.4, 144.8) |
( 41.5, 120.6) ( 44.5, 109.7) ( 38.9, 93.5) ( 49.8, 136.8) ( 45.6, 107.6) |
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( 33.0, 102.9) |
(47.6, 102.9) |
(32.5, 116.7) ( 42.0, 134.0) ( 54.1, 157.9) ( 35.4, 109.1) |
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( 37.9, |
92.4) ( 38.6, 120.7) ( 35.6, 96.1) ( 33.6, 73.2) ( 27.7, 61.5) ( 47.1, 95.0) |
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( 29.9, |
82.8) ( 50.1, 110.5) |
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Задача 6. |
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Выборка 1: |
63 28 92 36 90 40 7 75 53 12 14 30 17 93 86 64 |
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Выборка 2: |
58 31 4 60 30 |
92 59 27 82 56 52 95 54 8 49 36 |
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Вариант №2
Задача 1.
34.036.1 34.3 34.4 34.1 35.6 35.9 34.4 35.2 34.2 35.8 35.2 34.3 34.8 35.1
34.534.6 34.2 34.4 34.2 34.8 35.0 34.8 37.7 34.3 36.0 36.0 35.1 34.2 34.2
34.434.3 34.0 34.0 36.4 34.1 35.1 34.7 34.1 34.1 34.2 34.2 34.6 35.0 36.5
34.134.4 34.2 34.6 35.0 34.1 35.0 34.6 34.3 34.3 34.3 34.1 36.5 34.2 34.8
34.534.8 34.1 36.2 34.0 34.2 34.7 35.8 35.1 35.3 34.4 35.2 35.9 35.7 34.7
34.935.0 35.8 35.1 35.5 34.8 34.8 36.4 34.9 34.5 34.5 34.6 34.4 35.0 34.1
35.234.6 34.3 34.9 34.1 34.2 35.1 37.5 35.1 34.0
Задача 2.
X 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 Y 1.1 0.7 3.1 6.9 19.8 55.2 147.4 404.2 1096.8 2981.5
Задача 3.
γ = 0.999 8.0 -1.1 13.5 10.0 2.4 4.1 20.0 12.4 13.4 4.8 7.8 0.0 10.9 13.7 6.6
Задача 4. |
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s = 7, γ = 0.99 |
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13.4 |
8.6 |
22.1 |
2.3 |
14.6 |
13.0 |
11.1 |
29.4 |
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23.3 |
1.7 |
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2.1 |
21.6 |
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6.1 |
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6.6 |
16.0 |
11.6 |
16.6 |
1.6 |
15.8 |
18.9 |
10.6 |
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11.9 |
0.1 |
10.7 |
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3.8 |
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4.5 |
17.7 |
10.8 |
19.6 |
18.5 |
15.5 |
9.3 |
21.7 |
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10.5 |
10.4 |
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8.2 |
16.0 |
22.6 |
20.5 |
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11.6 |
23.2 |
23.0 |
9.5 |
11.3 |
14.9 |
19.9 |
13.4 |
13.9 |
19.5 |
19.8 |
21.0 |
3.2 |
14.0 |
19.1 |
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17.9 |
8.6 |
11.2 |
16.2 |
13.9 |
16.2 |
17.1 |
7.7 |
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20.2 |
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16.5 |
12.3 |
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17.6 |
6.6 |
20.3 |
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9.8 |
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15.5 |
16.2 |
18.4 |
9.2 |
5.7 |
10.9 |
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16.2 |
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Задача 5.
( 50.0, -92.8) ( 27.4, -49.5) ( 47.7,-105.8) ( 35.1, -67.0) ( 30.5, -55.7) ( 39.5, -67.3) ( 54.8, -89.1) ( 57.3,-134.2) (43.0,-109.1) ( 43.7, -68.7) ( 34.6, -74.6) ( 47.2,-105.6) ( 42.4,-106.2) ( 57.6,-164.1) ( 38.8, -59.7) ( 37.3, -81.7) (35.5, -67.2) ( 41.9,-119.3) ( 23.0, -64.2) ( 45.3, -96.5) ( 51.5,-148.9) ( 50.9,-118.5) (58.6,-151.8) ( 33.6, -65.7) ( 31.2, -83.0) ( 35.3, -68.9) ( 49.8, -87.0) ( 38.5, -58.9) ( 32.9, -71.8) ( 54.4,-103.4) ( 39.3, -58.7) ( 46.0,-107.7) ( 25.0, -43.4) ( 31.6, -70.0) ( 29.0, -76.4) ( 27.4, -56.9) ( 46.4,-111.0) ( 35.0, -71.5) ( 39.5,-104.4) ( 27.1, -47.6)
Задача 6.
Выборка 1: 93 70 90 61 14 79 60 50 39 6 Выборка 2: 64 61 58 54 24 42 5 19 45 7
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Вариант №3
Задача 1.
12.812.3 14.7 12.2 13.2 12.0 15.2 13.2 12.3 13.7 14.3 12.5 12.2 13.9 16.2
14.413.0 12.3 12.3 15.1 14.2 12.5 15.9 12.0 14.8 12.1 19.9 12.8 12.8 12.8
14.415.7 12.2 12.2 15.0 12.4 12.5 12.9 13.6 12.2 13.4 12.1 13.1 12.6
14.213.6 12.0 16.4 12.3 14.2 14.1 12.2 13.3 12.4 12.6 13.5 14.8 12.6 21.8
12.914.1 12.5 13.8 19.1 15.8 13.8 14.8 15.1 12.0 13.3 17.5 15.8 13.3 12.3
12.814.0 12.9 12.7 16.2 14.5 19.0 20.0 13.5 13.3 13.1 12.7 13.0 17.0 18.7
17.012.6 13.1 12.9 12.2 12.9 15.3 13.7 12.6 12.3 18.8
Задача 2. |
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X |
1.0 |
2.0 |
3.0 |
4.0 |
5.0 |
6.0 |
7.0 |
8.0 |
9.0 |
10.0 |
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0.8 |
0.2 |
3.6 |
7.3 |
19.2 |
53.7 |
147.6 |
404.2 |
1096.2 |
2981.2 |
Задача 3.
γ = 0.95 31.6 34.9 46.9 42.8 36.0 26.2 28.6 48.5 27.7 45.8 32.0 41.2 39.8 33.1 36.3
53.5 43.9 35.8 32.9 34.4
Задача 4. |
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s = 6, γ = 0.95 |
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23.1 |
10.3 |
0.1 |
4.9 |
6.3 |
5.4 |
8.6 |
5.1 |
5.2 |
0.7 |
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1.9 |
7.1 |
4.8 |
9.3 |
2.3 |
6.8 |
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4.2 |
4.5 |
3.2 |
8.2 |
2.2 -0.3 13.0 |
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2.4 |
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12.7 |
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12.2 -0.3 10.3 7.3 7.7 8.3 |
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9.1 |
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4.3 |
-4.3 -1.0 -6.6 |
1.4 4.7 9.0 4.5 16.7 -1.6 |
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12.4 |
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6.8 |
13.0 |
7.6 |
-0.7 |
11.9 |
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11.6 |
15.2 |
1.0 11.1 |
5.7 11.2 |
0.3 4.7 |
8.3 |
1.6 |
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3.0 |
4.7 10.4 |
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5.2 |
2.2 |
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10.4 |
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11.2 |
4.8 |
10.3 |
8.2 |
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Задача 5.
( 62.1, -89.2) (17.3, -40.6) ( 36.8, -81.4) ( 31.3, -50.0) ( 33.7, -56.3) ( 36.0, -49.6) ( 48.5, -65.2) ( 16.3, -22.2) ( 22.3, -47.2) ( 32.2, -70.4) ( 48.0, -87.9) ( 27.0, -45.5) ( 36.1, -49.7) ( 35.6, -65.8) ( 39.7, -84.2) ( 23.9, -53.5) ( 49.2, -83.7) ( 22.4, -27.8) ( 23.4, -51.7) (35.7, -83.6) ( 46.0,-101.2) ( 52.4,-109.1) ( 43.9,-106.1) ( 44.5, -68.3) ( 28.0, -47.8) ( 52.3, -72.5) ( 27.7, -63.7) ( 30.8, -41.7) ( 38.5, -75.4) ( 44.2, -55.9) ( 21.5, -49.9) ( 32.3, -71.8) ( 81.7,-110.2) ( 31.1, -52.8) ( 48.0, -63.8) ( 34.1, -82.2) ( 41.6, -58.1) ( 41.1, -73.4) ( 34.5, -65.4) ( 52.3, -78.1) ( 51.5,-121.0) ( 27.5, -58.8)
Задача 6.
Выборка 1: 61 85 36 80 53 71 65 83 18 Выборка 2: 51 25 89 32 85 37 62 47 43
15
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Вариант №4
Задача 1. |
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40.2 |
31.8 |
31.2 |
29.1 |
25.7 |
37.5 |
49.1 |
28.9 |
36.7 |
30.6 |
44.1 |
31.1 |
44.9 |
40.0 |
31.0 |
50.9 |
41.3 |
46.0 |
33.8 |
28.0 |
30.9 |
34.5 |
48.8 |
32.3 |
40.9 |
35.8 |
43.8 |
28.1 |
27.0 |
33.0 |
29.8 |
28.5 |
28.8 |
33.4 |
32.5 |
46.6 |
39.4 |
38.6 |
41.6 |
41.4 |
36.1 |
31.8 |
47.6 |
34.0 |
28.2 |
28.2 |
42.1 |
39.2 |
42.0 |
24.0 |
24.2 |
28.1 |
48.4 |
37.7 |
36.4 |
38.9 |
35.3 |
38.9 |
44.1 |
45.3 |
28.9 |
26.4 |
46.4 |
35.4 |
36.6 |
36.6 |
29.3 |
33.7 |
25.0 |
33.3 |
28.0 |
46.2 |
28.0 |
41.7 |
31.3 |
24.1 |
26.7 |
31.0 |
33.3 |
30.8 |
32.2 |
29.3 |
36.2 |
45.8 |
26.6 |
45.2 |
49.9 |
33.6 |
46.1 |
47.8 |
41.6 |
24.6 |
47.4 |
25.7 |
31.2 |
38.2 |
42.5 |
40.3 |
26.6 |
39.8 |
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Задача 2. |
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X |
2.0 |
3.0 |
4.0 |
5.0 |
6.0 |
7.0 |
8.0 |
9.0 |
10.0 |
11.0 |
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Y |
3.0 |
3.7 |
4.2 |
4.8 |
4.8 |
5.3 |
5.0 |
6.3 |
7.2 |
6.8 |
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Задача 3. |
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γ = 0.999 |
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25.4 |
31.1 |
13.2 |
23.0 |
19.1 |
26.5 |
23.2 |
29.2 |
24.8 |
26.6 |
29.3 |
21.4 |
28.2 |
38.2 |
19.9 |
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30.6 |
24.5 |
23.2 |
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Задача 4. |
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s = 6, γ = 0.95 |
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35.5 |
11.9 |
17.0 |
19.6 |
20.4 |
23.7 |
20.8 |
23.6 |
20.6 |
27.5 |
24.6 |
29.1 |
20.8 |
30.0 |
17.2 |
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38.7 |
19.2 |
18.8 |
28.3 |
25.9 |
28.5 |
22.6 |
21.4 |
18.1 |
26.3 |
10.5 |
22.6 |
22.5 |
28.2 |
27.2 |
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19.616.4 26.3 23.2 35.1 22.5 29.1 23.7 22.8 19.9 30.8 33.6 20.5 17.3 34.5
25.223.0 29.0 19.7 20.2 27.0 29.1 32.5 25.7 18.5 31.6 23.1 26.2 17.4 32.2
19.721.5 25.9 17.6 24.7 13.1 22.9 25.8 25.8 27.2 30.8 28.7 16.9 21.7 20.6
29.722.1 32.5 26.7 23.3 39.6 17.7 20.7 9.6 21.5 24.8 28.0 26.2 28.4 26.8
24.922.3 30.2 26.7 21.9 35.1 16.7 31.0 20.5 29.1
Задача 5.
( 40.2,-135.8) (48.5,-145.2) (56.4,-128.6) (53.3,-119.6) (44.1,-134.1) ( 46.4,-129.0) ( 42.9,-129.7) (47.1,-123.1) (57.5,-153.4) (50.5,-153.6) ( 40.4, -77.5) ( 43.2,-124.7) ( 59.6,-148.4) (54.8,-159.3) (45.2, -88.2) (39.4,-109.7) ( 37.9,-123.5) ( 45.4,-165.9) ( 41.5, -85.9) ( 34.3,-109.3) (47.6,-129.4) (47.6,-167.8) ( 57.1,-202.7) ( 35.0, -66.6) ( 35.6, -69.1) (53.5,-147.7) (47.7,-171.0) (41.3,-132.0) ( 53.4,-134.8) ( 47.0,-132.3) (39.7, -74.7) ( 36.7,-120.6) ( 48.6, -91.7) ( 43.6,-102.1) ( 38.8,-135.7) ( 39.8, -90.6) ( 43.2,-156.7) ( 39.5, -80.0) ( 42.0,-105.3) ( 51.7,-177.1)
Задача 6.
Выборка 1: 3 26 29 15 11 23 81 86 80 46 10 34 Выборка 2: 37 97 45 14 95 27 75 99 24 23 60 2
16
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Вариант №5 |
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Задача 1. |
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14.6 |
15.2 |
14.1 |
14.1 |
15.0 |
14.0 |
15.0 |
15.1 |
15.5 |
15.9 |
15.5 |
14.2 |
14.0 |
14.5 |
14.7 |
15.5 |
15.5 |
14.2 |
14.4 |
14.4 |
14.4 |
16.4 |
15.7 |
14.4 |
14.1 |
15.5 |
14.9 |
15.1 |
15.1 |
14.8 |
14.4 |
16.3 |
14.1 |
14.1 |
14.6 |
14.2 |
14.9 |
14.7 |
14.8 |
15.5 |
16.4 |
14.6 |
14.5 |
14.9 |
14.2 |
15.1 |
14.4 |
16.0 |
16.3 |
15.5 |
15.8 |
18.3 |
14.2 |
16.0 |
14.9 |
14.0 |
14.2 |
14.2 |
14.2 |
14.9 |
14.8 |
14.4 |
15.8 |
14.1 |
15.4 |
14.8 |
14.2 |
14.0 |
14.4 |
16.2 |
14.6 |
14.0 |
17.4 |
15.9 |
15.3 |
14.4 |
14.0 |
14.1 |
15.4 |
15.4 |
14.4 |
15.5 |
14.8 |
15.7 |
14.1 |
14.7 |
14.6 |
14.4 |
14.2 |
16.6 |
14.0 |
14.1 |
15.7 |
14.8 |
14.1 |
14.6 |
14.0 |
14.1 |
15.5 |
15.4 |
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Задача 2. |
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X |
1.0 |
2.0 |
3.0 |
4.0 |
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5.0 |
6.0 |
7.0 |
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8.0 |
9.0 |
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10.0 |
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Y |
0.1 |
1.5 |
2.8 |
8.2 |
20.2 |
55.4 |
147.5 |
403.0 |
1097.6 |
2980.0 |
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Задача 3. |
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γ = 0.95 |
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10.5 |
5.5 |
12.6 |
27.0 |
25.0 |
31.2 |
15.9 |
15.3 |
17.4 |
32.8 |
30.3 |
9.5 |
17.7 |
16.4 |
15.9 |
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Задача 4. |
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s = 5, γ = 0.95 |
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41.9 |
34.5 |
38.3 |
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35.0 |
31.0 |
38.5 |
36.4 |
36.8 |
38.8 |
37.0 |
45.4 |
39.3 |
46.2 |
42.9 |
35.0 |
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36.3 |
41.7 |
33.6 |
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37.9 |
40.0 |
35.9 |
43.4 |
43.3 |
31.3 |
26.9 |
40.4 |
40.5 |
37.9 |
32.4 |
35.2 |
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38.4 |
38.1 |
34.5 |
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37.0 |
39.8 |
33.7 |
37.2 |
41.1 |
37.0 |
41.8 |
39.0 |
42.6 |
32.7 |
45.3 |
40.9 |
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37.1 |
31.7 |
36.2 |
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35.5 |
29.6 |
38.3 |
42.2 |
34.2 |
40.5 |
28.6 |
32.1 |
37.9 |
36.2 |
43.0 |
31.7 |
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35.4 |
32.2 |
42.6 |
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40.1 |
35.8 |
44.8 |
32.9 |
31.4 |
41.9 |
48.4 |
45.0 |
38.1 |
43.0 |
31.1 |
42.5 |
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51.8 |
42.3 |
35.2 |
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38.2 |
45.3 |
29.9 |
34.6 |
38.7 |
29.0 |
31.9 |
28.6 |
36.6 |
37.4 |
32.5 |
32.3 |
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40.2 |
40.9 |
35.5 |
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31.6 |
39.1 |
36.8 |
34.9 |
41.1 |
41.4 |
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40.6 |
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Задача 5.
(25.0, 101.1) ( 46.4, 123.7) ( 44.8, 131.2) ( 40.7, 143.4) (17.5, 59.9) ( 27.8, 96.8) ( 35.0, 71.2) ( 37.1, 99.0) (47.1, 135.5) ( 23.2, 63.7) ( 38.8, 85.4) ( 29.2, 105.4) (39.8, 131.1) ( 34.9, 115.1) ( 59.1, 149.8) ( 30.9, 62.9) (38.3, 150.5) ( 38.8, 151.8) ( 58.1, 205.8) (50.9, 110.8) ( 65.7, 253.4) ( 35.3, 111.3) ( 49.8, 162.4) ( 23.3, 83.1)
( 31.6, 126.7) ( 37.9, 91.8) ( 26.1, |
67.9) ( 37.3, 108.7) (31.5, |
96.9) ( 66.0, 134.9) |
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( 41.4, 164.0) ( 46.9, 120.0) ( 45.2, |
93.4) ( 50.3, 155.0) ( 26.1, |
72.9) ( 46.8, 96.8) |
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( 41.5, 103.5) ( 28.9, 110.6) ( 20.5, |
51.4) ( 35.9, 87.9) ( 28.8, 102.4) ( 45.0, 118.9) |
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( 47.3, 176.6) |
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Задача 6. |
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Выборка 1: |
95 64 66 88 63 57 5 89 61 58 87 93 14 |
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Выборка 2: |
90 36 65 16 7 94 1 93 12 11 44 92 13 |
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17
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Вариант №6
Задача 1. |
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40.6 |
29.8 |
27.6 |
32.5 |
36.1 |
28.4 |
30.2 |
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32.0 |
31.2 |
28.6 |
34.2 |
35.3 |
34.2 |
32.5 |
37.6 |
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31.0 |
32.2 |
37.4 |
32.4 |
31.5 |
32.2 |
32.8 |
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34.4 |
25.5 |
31.0 |
36.3 |
30.8 |
34.3 |
30.2 |
33.2 |
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32.5 |
29.3 |
32.1 |
30.1 |
36.5 |
27.2 |
34.0 |
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30.9 |
30.9 |
27.6 |
34.4 |
36.3 |
28.9 |
28.4 |
32.3 |
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34.7 |
30.0 |
29.2 |
31.7 |
30.4 |
36.6 |
28.5 |
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30.6 |
36.6 |
37.8 |
33.6 |
30.2 |
29.9 |
27.4 |
34.2 |
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32.1 |
25.5 |
30.9 |
31.6 |
29.8 |
33.9 |
29.0 |
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32.9 |
30.9 |
29.6 |
30.7 |
33.3 |
36.3 |
29.7 |
39.1 |
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33.2 |
27.7 |
33.6 |
32.1 |
35.4 |
32.2 |
27.7 |
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31.1 |
31.6 |
33.2 |
30.1 |
29.6 |
29.1 |
26.1 |
31.7 |
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33.9 |
32.6 |
31.4 |
28.8 |
35.5 |
28.8 |
36.6 |
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28.2 |
33.2 |
29.5 |
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Задача 2. |
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X |
7.0 |
8.0 |
9.0 |
10.0 |
11.0 |
12.0 |
13.0 |
14.0 |
15.0 |
16.0 |
17.0 |
18.0 |
19.0 |
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Y |
6.3 |
5.4 |
5.4 |
6.3 |
6.5 |
8.0 |
7.3 |
8.2 |
7.9 |
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7.7 |
9.3 |
8.5 |
9.6 |
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Задача 3. |
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γ = 0.999 |
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13.5 |
10.7 25.2 |
10.8 |
21.6 |
0.8 |
1.4 17.1 0.6 |
12.0 |
-4.5 |
2.2 11.0 22.9 |
4.7 9.5 |
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Задача 4. |
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s = 8, γ = 0.90 |
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13.7 |
32.5 |
11.0 |
11.0 |
20.1 |
1.6 |
29.6 |
37.9 |
35.1 |
45.5 |
21.6 |
21.1 |
4.8 |
13.9 |
25.6 |
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21.7 |
20.3 |
23.2 |
14.5 |
16.3 |
21.6 |
19.3 |
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24.4 |
16.3 |
11.6 |
33.9 |
7.5 |
16.5 |
4.4 |
32.1 |
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16.1 |
26.2 |
20.2 |
24.1 |
23.5 |
13.9 |
28.1 |
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19.2 |
34.8 |
14.3 |
7.4 |
9.4 |
30.1 |
14.2 |
6.9 |
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19.8 |
17.4 |
29.2 |
17.6 |
27.0 |
16.8 |
9.2 |
26.5 |
25.5 |
41.9 |
22.4 |
14.3 |
25.8 |
19.9 |
6.9 |
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14.5 |
27.7 |
25.5 |
14.5 |
11.1 |
26.2 |
20.5 |
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23.7 |
12.0 |
23.4 |
12.8 |
17.5 |
24.1 |
32.0 |
21.1 |
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23.2 |
-1.1 |
14.8 |
28.5 |
32.3 |
13.5 |
13.4 |
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8.0 |
12.8 |
27.0 |
9.5 25.5 |
15.0 |
22.9 |
26.4 |
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11.2 |
14.1 |
26.1 |
20.5 |
14.5 |
27.3 |
17.9 |
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24.4 |
16.5 |
23.2 |
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Задача 5. |
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( 28.4, 45.3) ( 19.4, |
26.3) ( 36.2, 58.9) ( 29.2, 59.6) ( 29.8, 64.8) ( 31.0, 47.6) |
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( 41.0, 82.3) ( 21.9, |
26.8) ( 32.2, 64.8) ( 39.0, 81.2) ( 24.6, 35.1) ( 22.7, 32.7) |
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( 26.0, 41.8) ( 39.1, |
53.4) ( 40.4, |
64.5) ( 38.6, |
75.2) ( 33 .7, 46.6) (41.6, |
64.1) |
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( 33.6, 79.6) ( 17.8, |
28.6) ( 35.2, 64.3) ( 39.1, 72.8) ( 39.0, 59.9) ( 30.9, 58.7) |
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( 21.4, 42.5) ( 48.1, |
98.5) ( 29.4, |
56.8) ( 22.1, |
35.6) ( 28.1, |
61.0) ( 38.3, |
78.0) |
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( 29.7, |
55.1) ( 62.2, 110.4) ( 39.6, 73.1) |
( 27.1, 58.3) ( 40.0, 73.3) ( 30.2, 47.2) |
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22.6) ( 36.2, 49.7) ( 28.1, 38.3) ( 30.2, 53.5) ( 19.5, 43.7) ( 31.1, 73.7) |
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Задача 6. |
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Выборка 1: |
32 35 74 29 53 3 41 18 56 |
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Выборка 2: |
32 99 70 78 46 10 36 12 64 |
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18
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Вариант №7
Задача 1.
28.1 31.9 26.2 31.2 26.3 23.8 22.9 23.1 34.1 26.8 28.6 31.5 27.5 33.9 24.9
28.6 30.6 27.6 25.0 28.0 26.4 26.8 28.9 27.4 24.4 22.7 23.0 24.9 25.7 23.5
26.1 22.7 28.4 35.4 29.6 25.1 26.1 25.6 28.2 35.3 33.0 39.1 29.5 36.2 24.7
23.6 38.6 23.0 22.4 34.6 31.2 38.3 24.5 27.9 25.3 22.6 34.2 24.2 25.9 30.9
25.5 24.5 24.9 30.6 27.8 23.0 33.3 32.5 28.5 24.0 22.2 25.6 23.1 35.7 28.6
36.025.9 22.2 32.5 25.2 28.2 30.9 25.2 43.1 27.0 23.5 26.2 22.4 27.0 35.3
36.124.2 28.0 37.3 33.7 29.0 41.4 24.1 27.2 22.8
Задача 2. |
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X |
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8.0 |
9.0 |
10.0 |
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11.0 |
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12.0 |
13.0 |
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14.0 |
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15.0 |
16.0 |
17.0 |
18.0 |
19.0 |
20.0 |
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Y |
25.6 35.1 |
48.7 |
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63.2 |
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81.5 |
99.2 |
120.2 143.9 168.1 196.3 225.6 256.9 288.6 |
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Задача 3. |
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γ = 0.999 |
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9.4 |
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21.2 |
9.3 |
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9.7 |
14.4 |
5.8 |
18.7 |
8.2 |
13.4 |
6.5 |
17.2 |
5.9 |
2.2 |
5.0 |
3.3 |
15.6 |
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Задача 4. |
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s = 6, γ = 0.99 |
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42.9 |
33.4 |
34.7 |
37.7 |
37.6 |
32.3 |
50.1 |
42.7 |
41.6 |
39.0 |
29.4 |
38.5 |
28.6 |
44.5 |
41.2 |
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37.4 |
48.8 |
48.2 |
46.3 |
37.8 |
37.2 |
36.0 |
46.0 |
38.9 |
35.5 |
42.8 |
40.8 |
41.8 |
29.3 |
34.5 |
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31.4 |
41.1 |
41.4 |
46.1 |
41.3 |
44.4 |
47.6 |
40.5 |
34.8 |
37.5 |
37.4 |
46.1 |
40.2 |
39.0 |
41.2 |
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33.3 |
39.7 |
38.3 |
39.9 |
43.1 |
42.8 |
39.9 |
48.1 |
29.9 |
37.2 |
30.6 |
40.3 |
37.0 |
47.5 |
36.3 |
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36.0 |
49.0 |
48.0 |
30.6 |
44.6 |
36.3 |
44.7 |
35.9 |
42.7 |
38.5 |
42.4 |
33.5 |
31.3 |
53.1 |
49.4 |
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33.8 |
43.9 |
33.6 |
38.5 |
34.3 |
41.5 |
45.8 |
37.0 |
47.9 |
43.9 |
35.9 |
43.9 |
46.7 |
41.0 |
45.0 |
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38.9 |
33.6 |
36.7 |
45.1 |
34.8 |
40.5 |
41.4 |
27.3 |
36.4 |
41.8 |
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Задача 5.
( 43.0,-122.1) (61.7,-203.7) (36.9,-112.6) (62.5,-134.8) ( 40.9,-117.7) ( 38.2, -78.0) (47.5,-138.2) (62.8,-137.8) ( 42.1, -81.5) ( 67.2,-143.9) ( 42.7, -85.2) ( 48.2,-110.3) (35.1, -91.5) ( 47.3,-165.1) ( 38.0,-123.0) ( 37.1, -95.2) ( 39.3, -96.9) ( 54.4,-148.5) (32.8,-108.4) (51.3,-118.6) (44.8,-110.5) (52.4,-152.5) ( 76.2,-242.1) ( 57.0,-180.0) (44.2, -91.3) (46.8,-128.0) (61.6,-163.5) ( 52.8,-114.0) ( 63.9,-195.8) ( 43.7,-114.5) (67.4,-224.4) (44.0,-103.8) (54.1,-105.8) ( 39.4,-135.4) ( 52.6,-155.6) ( 51.5, -95.1) (54.6,-153.7) (55.8,-145.3) (52.5,-173.9) ( 74.4,-195.9) ( 34.5, -97.5) ( 57.2,-179.3) ( 46.1,-145.1)
Задача 6.
Выборка 1: 99 53 48 2 80 56 72 17 49 27 Выборка 2: 100 54 33 14 67 6 21 10 97 27
19
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Вариант №8
Задача 1.
25.6 29.3 24.0 26.5 27.1 25.2 29.1 24.0 29.6 27.6 30.3 25.1 26.1 24.2 25.9
27.5 31.5 25.7 26.5 24.1 28.4 24.2 28.4 24.2 25.3 24.4 25.0 28.6 24.9 29.3
30.6 24.1 26.0 25.4 26.6 24.4 25.2 24.4 24.5 25.4 26.0 25.9 24.0 27.4 24.4
24.2 33.6 24.5 24.4 24.1 28.3 24.7 25.0 26.4 27.4 24.4 29.5 27.2 25.0 26.0
37.1 27.9 25.4 26.1 25.7 30.5 27.3 28.0 26.3 29.3 26.4 27.6 33.5 24.8 24.6
30.1 25.3 24.2 28.9 25.9 24.9 25.8 27.3 25.4 25.4 28.2 25.7 24.0 29.4 24.2
27.7 30.9 36.6 26.7 32.4 26.3 24.6 39.6 24.2 25.8
Задача 2. |
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X |
9.0 |
10.0 |
11.0 |
12.0 |
13.0 |
14.0 |
15.0 |
16.0 |
17.0 |
18.0 |
19.0 |
Y80.5 100.6 120.0 144.3 169.0 195.2 224.5 255.6 289.9 323.3 361.4
Задача 3.
γ = 0.99 18.6 30.6 29.4 32.1 23.1 32.5 32.9 27.7 32.5 38.4 27.9 19.6 27.5 31.9 42.9
32.9 33.6 25.8 39.9 48.9
Задача 4. |
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s = 7, γ = 0.90 |
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-0.1 -2.9 |
-1.1 |
-1.7 |
9.6 |
11.6 |
9.1 |
1.3 |
10.1 1.1 |
8.8 |
12.8 -6.9 14.5 5.8 |
5.9 |
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18.1 |
20.4 |
6.0 |
-0.3 |
6.8 |
10.0 |
17.8 -0.4 17.3 16.3 12.3 |
9.8 |
0.3 |
8.9 |
10.8 |
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24.6 |
5.4 8.0 7.9 4.3 |
5.3 |
0.2 -1.0 11.7 14.3 |
29.2 7.1 9.4 7.5 -12.8 13.5 |
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15.0 |
5.2 |
11.5 |
1.9 |
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12.6 |
6.8 |
6.9 7.5 -6.0 4.7 |
17.5 18.2 13.3 17.5 |
6.6 |
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0.4 |
7.4 |
7.6 |
14.9 |
18.8 |
8.3 |
3.1 |
-3.7 |
3.3 |
-2.6 |
3.9 |
7.6 |
7.5 |
20.9 |
16.3 12.7 |
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7.8 |
0.5 |
2.6 |
14.1 |
-2.4 |
1.5 -4.1 |
2.5 |
4.7 |
-2.5 |
3.2 |
1.5 |
2.3 |
2.3 |
9.0 |
2.1 - |
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5.2 |
22.2 |
4.7 |
17.2 |
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3.2 |
2.6 |
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Задача 5.
(38.4,-115.7) (52.6,-113.5) ( 38.8,-126.5) ( 12.1, -34.6) ( 44.9,-164.8) ( 21.4, -51.1) ( 26.0, -85.3) ( 24.9, -84.7) ( 34.7, -91.3) ( 35.3,-124.1) ( 17.5, -36.6) ( 25.0, -72.3) ( 15.4, -47.6) ( 31.6, -68.4) ( 35.3, -71.9) ( 19.6, -63.7) ( 41.5,-110.4) ( 47.0,-108.3) (36.2,-128.4) (25.5, -92.9) ( 39.9,-136.0) ( 33.7, -91.1) ( 34.8,-114.5) ( 29.8,-100.4) ( 27.9, -65.7) ( 36.5, -71.4) ( 19.3, -37.8) ( 13.6, -38.6) ( 32.2,-117.6) ( 22.6, -82.4) ( 33.4, -79.5) ( 16.0, -39.0) ( 23.6, -63.8) ( 35.8, -94.1) ( 33.2, -80.0) ( 36.4,-101.8) ( 34.3,-117.3) ( 44.7,-170.2) ( 51.0,-143.3) ( -0.7, 7.9) ( 19.9, -41.2) ( 24.8, -79.7) ( 29.0, -75.3) ( 43.8,-166.4)
Задача 6.
Выборка 1: 60 25 76 17 95 9 1 57 94 Выборка 2: 54 42 7 46 26 62 69 20 16
20
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