VI. Непрерывная случайная величина х задана интегральной функцией
распределения. Найти:
а) дифференциальную
функцию
(плотность распределения вероятности);
б) вероятность
попадания случайной величины в интервал
;
в) математическое ожидание и дисперсию;
г) построить графики
,
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VII. По наблюдениям над признаком Х составлено статистическое распределение выборки. Построить полигон относительных частот и кумулятивную кривую. Найти эмпирическую функцию и построить ее график. Вычислить выборочное среднее, дисперсию и среднее квадратическое отклонение.
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12 |
15 |
17 |
20 |
24 |
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2. |
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18 |
21 |
25 |
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4 |
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10 |
8 |
3 |
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6 |
11 |
9 |
4 |
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3. |
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11 |
14 |
16 |
19 |
13 |
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4. |
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9 |
10 |
21 |
28 |
29 |
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3 |
4 |
9 |
7 |
2 |
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2 |
4 |
8 |
3 |
11 |
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5. |
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10 |
13 |
16 |
20 |
24 |
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6. |
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10 |
13 |
15 |
18 |
13 |
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3 |
2 |
5 |
7 |
6 |
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2 |
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8 |
6 |
1 |
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7. |
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6 |
9 |
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13 |
18 |
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8. |
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18 |
19 |
22 |
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2 |
6 |
3 |
10 |
7 |
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6 |
2 |
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5 |
8 |
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9. |
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5 |
6 |
8 |
9 |
12 |
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10. |
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13 |
15 |
19 |
22 |
25 |
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2 |
8 |
3 |
4 |
6 |
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2 |
8 |
3 |
1 |
9 |
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11. |
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16 |
18 |
22 |
27 |
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12. |
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15 |
19 |
21 |
23 |
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3 |
9 |
11 |
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4 |
9 |
13 |
12 |
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14 |
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23 |
26 |
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14. |
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18 |
19 |
22 |
27 |
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2 |
4 |
9 |
3 |
12 |
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7 |
3 |
16 |
2 |
14 |
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15. |
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15 |
19 |
22 |
28 |
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16. |
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11 |
15 |
16 |
19 |
24 |
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6 |
2 |
7 |
2 |
10 |
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5 |
1 |
13 |
14 |
8 |
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17. |
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3 |
9 |
12 |
20 |
26 |
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18. |
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9 |
11 |
13 |
19 |
20 |
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5 |
1 |
9 |
18 |
15 |
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5 |
11 |
9 |
6 |
8 |
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19. |
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12 |
15 |
19 |
23 |
29 |
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20. |
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6 |
12 |
15 |
18 |
22 |
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8 |
3 |
1 |
5 |
2 |
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5 |
12 |
4 |
8 |
1 |
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21. |
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8 |
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19 |
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22. |
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19 |
22 |
26 |
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2 |
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3 |
15 |
1 |
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2 |
13 |
4 |
3 |
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23. |
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18 |
20 |
25 |
27 |
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24. |
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10 |
11 |
16 |
19 |
21 |
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5 |
2 |
4 |
17 |
3 |
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2 |
1 |
5 |
16 |
14 |
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25. |
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10 |
15 |
25 |
27 |
29 |
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26. |
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14 |
16 |
17 |
19 |
25 |
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13 |
15 |
17 |
6 |
4 |
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3 |
4 |
9 |
12 |
8 |
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27. |
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9 |
12 |
16 |
21 |
26 |
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28. |
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17 |
19 |
21 |
23 |
27 |
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9 |
2 |
14 |
13 |
5 |
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1 |
9 |
7 |
14 |
19 |
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29. |
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12 |
16 |
19 |
22 |
27 |
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30. |
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16 |
20 |
21 |
23 |
26 |
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6 |
21 |
13 |
5 |
17 |
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2 |
8 |
14 |
13 |
5 |
VIII. В предположении о нормальном распределении признака построить теоретические частоты с помощью интегральной функции распределения и плотность вероятности. Проверить на основе критериев Пирсона, Колмогорова, Романовского согласованность фактических и теоретических частот
1.
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1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
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2 |
8 |
26 |
65 |
120 |
181 |
201 |
170 |
120 |
64 |
28 |
10 |
3 |
2.
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2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
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1 |
6 |
19 |
47 |
86 |
130 |
145 |
122 |
86 |
46 |
20 |
7 |
2 |
3.
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3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
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1 |
4 |
14 |
34 |
62 |
94 |
105 |
88 |
62 |
33 |
15 |
5 |
2 |
4.
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4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
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6 |
20 |
49 |
90 |
136 |
151 |
128 |
90 |
48 |
21 |
8 |
2 |
5.
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5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
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2 |
7 |
21 |
53 |
98 |
148 |
165 |
139 |
98 |
52 |
23 |
8 |
2 |
6.
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6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
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1 |
6 |
19 |
48 |
89 |
135 |
150 |
127 |
89 |
48 |
21 |
7 |
2 |
7.
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7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
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2 |
6 |
20 |
50 |
92 |
139 |
155 |
131 |
92 |
49 |
22 |
8 |
2 |
8.
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|
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
20-21 |
|
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2 |
7 |
22 |
55 |
101 |
152 |
169 |
143 |
101 |
54 |
24 |
8 |
3 |
9.
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9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
20-21 |
21-22 |
|
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2 |
6 |
21 |
53 |
97 |
147 |
163 |
138 |
97 |
52 |
23 |
8 |
2 |
10.
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10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
20-21 |
21-22 |
22-23 |
|
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2 |
7 |
23 |
58 |
107 |
161 |
179 |
151 |
107 |
57 |
25 |
9 |
3 |
11.
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|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
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1 |
6 |
18 |
45 |
83 |
126 |
140 |
118 |
83 |
44 |
19 |
7 |
2 |
12.
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|
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
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2 |
7 |
24 |
59 |
109 |
164 |
182 |
154 |
109 |
58 |
25 |
9 |
3 |
13.
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3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
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2 |
7 |
22 |
56 |
103 |
156 |
173 |
146 |
103 |
55 |
24 |
9 |
3 |
14.
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4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
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1 |
4 |
13 |
33 |
61 |
91 |
102 |
86 |
61 |
32 |
14 |
5 |
2 |
15.
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5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
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1 |
4 |
14 |
36 |
66 |
99 |
110 |
93 |
66 |
35 |
15 |
5 |
2 |
16.
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6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
|
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1 |
5 |
15 |
38 |
70 |
105 |
117 |
99 |
70 |
37 |
16 |
6 |
2 |
17.
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7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
|
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2 |
7 |
24 |
60 |
112 |
168 |
187 |
158 |
112 |
60 |
26 |
9 |
3 |
18.
|
|
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
20-21 |
|
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2 |
7 |
21 |
53 |
98 |
148 |
164 |
139 |
98 |
52 |
23 |
8 |
2 |
19.
|
|
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
20-21 |
21-22 |
|
|
2 |
7 |
23 |
58 |
107 |
162 |
180 |
152 |
107 |
57 |
25 |
9 |
3 |
20.
|
|
10-11 |
11-12 |
12-13 |
13-14 |
14-15 |
15-16 |
16-17 |
17-18 |
18-19 |
19-20 |
20-21 |
21-22 |
22-23 |
|
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2 |
7 |
23 |
57 |
106 |
159 |
177 |
150 |
106 |
56 |
25 |
9 |
3 |
21.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
8 |
33 |
108 |
271 |
500 |
754 |
838 |
708 |
500 |
267 |
117 |
42 |
13 |
22.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
6 |
24 |
78 |
195 |
360 |
543 |
603 |
510 |
360 |
192 |
84 |
30 |
9 |
23.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
4 |
17 |
56 |
141 |
260 |
392 |
436 |
368 |
260 |
139 |
61 |
22 |
7 |
24.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
6 |
25 |
81 |
203 |
375 |
566 |
628 |
531 |
375 |
200 |
88 |
31 |
9 |
25.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
7 |
27 |
89 |
222 |
410 |
618 |
687 |
581 |
410 |
219 |
96 |
34 |
10 |
26.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
6 |
25 |
81 |
202 |
373 |
562 |
624 |
528 |
373 |
199 |
87 |
31 |
9 |
27.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
6 |
26 |
83 |
209 |
385 |
581 |
645 |
545 |
385 |
205 |
90 |
32 |
10 |
28.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
7 |
28 |
91 |
228 |
420 |
634 |
704 |
595 |
420 |
224 |
98 |
35 |
11 |
29.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
7 |
27 |
88 |
219 |
405 |
611 |
678 |
574 |
405 |
216 |
95 |
34 |
10 |
30.
|
|
1-2 |
2-3 |
3-4 |
4-5 |
5-6 |
6-7 |
7-8 |
8-9 |
9-10 |
10-11 |
11-12 |
12-13 |
13-14 |
|
|
7 |
30 |
96 |
241 |
445 |
671 |
745 |
630 |
445 |
237 |
104 |
37 |
11 |
