- •Министерство образования Республики Беларусь
- •Задача 1.15
- •Решение:
- •Графики эмпирической и теоретической функции распределения
- •Теоретическая функция распределения
- •Задача 11.37
- •Решение:
- •Литература:
- •Задача 10.93
- •Решение:
- •Графики эмпирической и теоретической функции распределения
- •Теоретическая функция распределения
Решение:
Построим вариационный ряд. Отсортируем заданную совокупность значений по возрастанию:
-4.5 |
-4.44 |
-4.23 |
-4.17 |
-4.16 |
-4.01 |
-3.92 |
-3.89 |
-3.86 |
-3.79 |
-3.75 |
-3.72 |
-3.7 |
-3.69 |
-3.65 |
-3.59 |
-3.56 |
-3.46 |
-3.44 |
-3.42 |
-3.36 |
-3.33 |
-3.32 |
-3.21 |
-3.13 |
-3.11 |
-3.1 |
-3.04 |
-3.03 |
-3.03 |
-3 |
-2.81 |
-2.79 |
-2.75 |
-2.69 |
-2.68 |
-2.65 |
-2.58 |
-2.53 |
-2.52 |
-2.43 |
-2.35 |
-2.3 |
-2.29 |
-2.27 |
-2.26 |
-2.26 |
-2.07 |
-2.04 |
-2.01 |
-2 |
-1.74 |
-1.72 |
-1.72 |
-1.57 |
-1.55 |
-1.54 |
-1.49 |
-1.48 |
-1.26 |
-1.25 |
-1.21 |
-1.19 |
-1.11 |
-1.06 |
-1.02 |
-0.98 |
-0.92 |
-0.89 |
-0.84 |
-0.81 |
-0.62 |
-0.62 |
-0.6 |
-0.58 |
-0.51 |
-0.49 |
-0.34 |
-0.32 |
-0.28 |
-0.22 |
-0.22 |
-0.19 |
-0.08 |
-0.07 |
-0.07 |
-0.03 |
-0.02 |
-0.01 |
0 |
0.02 |
0.07 |
0.32 |
0.36 |
0.43 |
0.5 |
0.68 |
0.71 |
0.76 |
0.77 |
Построим эмпирическую функцию распределения:
где -аргумент (неслучайная величина);
-объем выборки
-количество значений в выборке или вариационном ряду, строго меньших
-4.5 |
-4.44 |
-4.23 |
-4.17 |
-4.16 |
-4.01 |
-3.92 |
-3.89 |
-3.86 |
-3.79 |
-3.75 |
-3.72 |
-3.7 |
-3.69 |
-3.65 | |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 | |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 | |
0 |
0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |
0.10 |
0.11 |
0.12 |
0.13 |
0.14 |
|
-3.59 |
-3.56 |
-3.46 |
-3.44 |
-3.42 |
-3.36 |
-3.33 |
-3.32 |
-3.21 |
-3.13 |
-3.11 |
-3.1 |
-3.04 |
-3.03 |
-3.03 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.15 |
0.16 |
0.17 |
0.18 |
0.19 |
0.20 |
0.21 |
0.22 |
0.23 |
0.24 |
0.25 |
0.26 |
0.27 |
0.28 |
0.29 |
-3 |
-2.81 |
-2.79 |
-2.75 |
-2.69 |
-2.68 |
-2.65 |
-2.58 |
-2.53 |
-2.52 |
-2.43 |
-2.35 |
-2.3 |
-2.29 |
-2.27 | |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 | |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 | |
0.30 |
0.31 |
0.32 |
0.33 |
0.34 |
0.35 |
0.36 |
0.37 |
0.38 |
0.39 |
0.40 |
0.41 |
0.42 |
0.43 |
0.44 |
-2.26 |
-2.07 |
-2.04 |
-2.01 |
-2 |
-1.74 |
-1.72 |
-1.57 |
-1.55 |
-1.54 |
-1.49 |
-1.48 |
-1.26 |
-1.25 |
-1.21 | |
2 |
1 |
1 |
1 |
1 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 | |
0.02 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.02 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 | |
0.45 |
0.47 |
0.48 |
0.49 |
0.50 |
0.51 |
0.52 |
0.54 |
0.55 |
0.56 |
0.57 |
0.58 |
0.59 |
0.60 |
0.61 |
|
-1.19 |
-1.11 |
-1.06 |
-1.02 |
-0.98 |
-0.92 |
-0.89 |
-0.84 |
-0.81 |
-0.62 |
-0.6 |
-0.58 |
-0.51 |
-0.49 |
-0.34 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
|
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.02 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.62 |
0.63 |
0.64 |
0.65 |
0.66 |
0.67 |
0.68 |
0.69 |
0.70 |
0.71 |
0.73 |
0.74 |
0.75 |
0.76 |
0.77 |
|
-0.32 |
-0.28 |
-0.22 |
-0.19 |
-0.08 |
-0.07 |
-0.03 |
-0.02 |
-0.01 |
0 |
0.02 |
0.07 |
0.32 |
0.36 |
0.43 |
|
1 |
1 |
2 |
1 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
0.01 |
0.01 |
0.02 |
0.01 |
0.01 |
0.02 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
0.78 |
0.79 |
0.80 |
0.82 |
0.83 |
0.84 |
0.86 |
0.87 |
0.88 |
0.89 |
0.90 |
0.91 |
0.92 |
0.93 |
0.94 |
|
0.5 |
0.68 |
0.71 |
0.76 |
0.77 |
>0.77 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
0.01 |
0.01 |
0.01 |
0.01 |
0.01 |
|
|
|
|
|
|
|
|
|
|
0.95 |
0.96 |
0.97 |
0.98 |
0.99 |
1 |
|
|
|
|
|
|
|
|
|