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0.000000 + 0.000000 + 1.000000 diff --git a/ex6.2.2/bin/data2.csv b/ex6.2.2/bin/data2.csv new file mode 100644 index 0000000..6e00d59 --- /dev/null +++ b/ex6.2.2/bin/data2.csv @@ -0,0 +1,10000 @@ + 1.000000 + 1.000000 + 0.000000 + 1.000000 + 2.000000 + 2.000000 + 0.000000 + 0.000000 + 0.000000 + 1.000000 + 0.000000 + 1.000000 + 1.000000 + 0.000000 + 1.000000 + 1.000000 + 0.000000 + 1.000000 + 0.000000 + 1.000000 + 0.000000 + 1.000000 + 1.000000 + 0.000000 + 1.000000 + 2.000000 + 0.000000 + 0.000000 + 1.000000 + 2.000000 + 3.000000 + 1.000000 + 2.000000 + 2.000000 + 1.000000 + 0.000000 + 1.000000 + 1.000000 + 1.000000 + 0.000000 + 1.000000 + 1.000000 + 0.000000 + 0.000000 + 1.000000 + 2.000000 + 1.000000 + 0.000000 + 0.000000 + 1.000000 + 0.000000 + 0.000000 + 1.000000 + 0.000000 + 1.000000 + 1.000000 + 1.000000 + 1.000000 + 1.000000 + 1.000000 + 1.000000 + 1.000000 + 1.000000 + 1.000000 + 0.000000 + 1.000000 + 0.000000 + 0.000000 + 3.000000 + 0.000000 + 1.000000 + 1.000000 + 1.000000 + 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0.000000 + 1.000000 + 2.000000 + 0.000000 + 1.000000 + 0.000000 + 2.000000 + 1.000000 diff --git a/ex6.2.2/bin/main.py b/ex6.2.2/bin/main.py new file mode 100644 index 0000000..0af7f8f --- /dev/null +++ b/ex6.2.2/bin/main.py @@ -0,0 +1,17 @@ + +def main(): + with open("data2.csv", 'r') as data: + s = 0 + c = 0 + for v in data: + s += float(v) + c += 1 + + E = s / c + p = E / c + print(f"p = {p}") + d = c * p * (1 - p) + print(f"d = {d}") + +if __name__ == "__main__": + main() diff --git a/ex7.1/data.csv b/ex7.1/data.csv new file mode 100644 index 0000000..51a4553 --- /dev/null +++ b/ex7.1/data.csv @@ -0,0 +1,81 @@ +Амурская область,43156 +Архангельская область,47526 +Астраханская область,32166 +Белгородская область,31163 +Брянская область,27403 +Владимирская область,31647 +Волгоградская область,30097 +Вологодская область,36081 +Воронежская область,31286 +г. Москва ,78946 +г. Санкт-Петербург,58310 +г. Севастополь,31008 +Забайкальский край,40728 +Ивановская область,26053 +Иркутская область,42921 +Кабардино-Балкарская Республика,25318 +Калининградская область,32473 +Калужская область,38005 +Камчатский край,71553 +Карачаево-Черкесская Республика,25699 +Кемеровская область,37857 +Кировская область,27580 +Костромская область,27948 +Краснодарский край,33258 +Красноярский край,44692 +Курганская область,27887 +Курская область,30125 +Ленинградская область,42434 +Липецкая область,30775 +Магаданская обл.,101662 +Московская обл.,50135 +Мурманская обл.,56005 +Ненецкий АО,77277 +Нижегородская область,32973 +Новгородская область,30820 +Новосибирская область,36048 +Омская область,32013 +Орловская область,26834 +Пензенская область,30112 +Пермский край,34809 +Приморский край,42026 +Псковская область,27339 +Республика Адыгея,27455 +Республика Алтай,37764 +Республика Башкортостан,33137 +Республика Бурятия,37867 +Республика Дагестан,24550 +Республика Ингушетия,25663 +Республика Калмыкия,25719 +Республика Карелия,39755 +Республика Коми,48316 +Республика Крым,28400 +Республика Марий Эл,28232 +Республика Мордовия,26999 +Республика Саха (Якутия),65881 +Республика Северная  Осетия - Алания,26108 +Республика Татарстан,35722 +Республика Тыва,35619 +Республика Хакасия,37949 +Ростовская область,30647 +Рязанская область,31192 +Самарская область,33086 +Саратовская область,26555 +Сахалинская обл.,73261 +Свердловская область,37605 +Смоленская область,29566 +Ставропольский край,28256 +Тамбовская область,26754 +Тверская область,30764 +Томская область,39707 +Тульская область,33933 +Удмуртская Республика,31990 +Ульяновская область,27927 +Хабаровский край,46583 +Ханты-Мансийский АО (Югра),62555 +Челябинская область,34944 +Чеченская Республика,26108 +Чувашская Республика,27028 +Чукотский АО,96930 +Ямало-Ненецкий АО,86560 +Ярославская область,33882 diff --git a/ex7.1/data.txt b/ex7.1/data.txt new file mode 100644 index 0000000..eb5a8cc --- /dev/null +++ b/ex7.1/data.txt @@ -0,0 +1,81 @@ +24550 +25318 +25663 +25699 +25719 +26053 +26108 +26108 +26555 +26754 +26834 +26999 +27028 +27339 +27403 +27455 +27580 +27887 +27927 +27948 +28232 +28256 +28400 +29566 +30097 +30112 +30125 +30647 +30764 +30775 +30820 +31008 +31163 +31192 +31286 +31647 +31990 +32013 +32166 +32473 +32973 +33086 +33137 +33258 +33882 +33933 +34809 +34944 +35619 +35722 +36048 +36081 +37605 +37764 +37857 +37867 +37949 +38005 +39707 +39755 +40728 +42026 +42434 +42921 +43156 +44692 +46583 +47526 +48316 +50135 +56005 +58310 +62555 +65881 +71553 +73261 +77277 +78946 +86560 +96930 +101662 diff --git a/ex7.1/data.xlsx b/ex7.1/data.xlsx new file mode 100644 index 0000000..099b6bf Binary files /dev/null and b/ex7.1/data.xlsx differ diff --git a/ex7.1/main.py b/ex7.1/main.py new file mode 100644 index 0000000..a31ef58 --- /dev/null +++ b/ex7.1/main.py @@ -0,0 +1,21 @@ + +def main() -> None: + with open("data.txt", 'r') as data: + nums = [int(v) for v in data] + # print(sum(nums)) + n = len(nums) + x_m = sum(nums) / n + print(f"x_m = {x_m}") + s_shifted = 0 + + for v in nums: s_shifted += (x_m - v) ** 2 + + s_shifted = s_shifted / n + + s_unshifted = s_shifted * n / (n - 1) + + print(f"смещенная дисперсия = {s_shifted}") + print(f"несмещенная дисперсия = {s_unshifted}") + +if __name__ == "__main__": + main() diff --git a/ex8.1/data.csv b/ex8.1/data.csv new file mode 100644 index 0000000..0acd1a9 --- /dev/null +++ b/ex8.1/data.csv @@ -0,0 +1,10000 @@ +5 +1 +1 +2 +2 +0 +1 +5 +0 +1 +4 +0 +1 +2 +3 +1 +2 +3 +1 +1 +3 +2 +4 +2 +3 +1 +3 +0 +4 +4 +2 +1 +2 +1 +4 +3 +0 +1 +4 +6 +0 +1 +3 +3 +0 +2 +4 +1 +2 +0 +2 +4 +2 +5 +0 +5 +1 +1 +0 +1 +3 +4 +2 +4 +1 +2 +1 +1 +1 +4 +5 +6 +3 +0 +1 +1 +0 +3 +0 +0 +2 +3 +2 +2 +2 +1 +0 +3 +2 +2 +2 +4 +2 +3 +3 +3 +2 +2 +3 +1 +2 +2 +2 +2 +0 +3 +7 +2 +3 +1 +3 +1 +0 +2 +0 +3 +3 +2 +4 +3 +4 +3 +2 +2 +6 +4 +0 +0 +2 +0 +4 +1 +1 +3 +3 +2 +1 +0 +1 +4 +0 +2 +1 +3 +2 +1 +4 +2 +3 +3 +2 +3 +3 +3 +4 +2 +1 +3 +4 +2 +5 +2 +2 +0 +1 +2 +0 +2 +3 +0 +6 +1 +0 +3 +0 +7 +0 +0 +1 +0 +2 +3 +4 +1 +1 +1 +5 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index 0000000..aefa85f --- /dev/null +++ b/exam_preview/main.py @@ -0,0 +1,24 @@ +import numpy as np +import matplotlib.pyplot as plt + + +def main() -> None: + + data = np.array([float(v) for v in open("data.csv", 'r')]) + + plt.figure(figsize=(8, 5)) + plt.hist(data, bins=10, density=True, edgecolor='black') + + plt.show() + + counts, bin_edges = np.histogram(data, bins=10) + print(f"число элементов в каждом интервале: {counts}") + # print(f"границы интервалов: {bin_edges}") + + S2 = np.var(data, ddof=1) + print(f"выборочная дисперсия: {S2}") + + + +if __name__ == "__main__": + main() diff --git a/theory/notes.pdf b/theory/notes.pdf new file mode 100644 index 0000000..2d62302 --- /dev/null +++ b/theory/notes.pdf @@ -0,0 +1,3431 @@ +%PDF-1.7 +% + +1 0 obj +<< + /Type /Pages + /Count 3 + /Kids [226 0 R 228 0 R 230 0 R] +>> +endobj + +2 0 obj +<< + /Type /Outlines + /First 3 0 R + /Last 11 0 R + /Count 9 +>> +endobj + +3 0 obj +<< + /Parent 2 0 R + /Next 4 0 R + /Title + /Dest 217 0 R 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block.with( + fill: luma(240), + inset: 10pt, + radius: 4pt, +) + + +#align(center)[= Распределения] + +#align(center)[ + #figure( + table(columns: 5, align: horizon, inset: 10pt)[*Распределение*][*Формула*][*$E[X]$*][*$V a r(X)$*][*Оценки*][Бернулли][$p^k (1 - p)^(1 - k)$][$p$][$p(1 - p)$][$p eq overline(X) \ theta_1 eq theta_2 eq overline(X) \ theta eq overline(X)$][Экспоненциальное][$cases(lambda e^(-lambda x) space.quad &x gt.eq 0, 0 space.quad &x lt 0)$][$1/lambda$][$1/(lambda^2)$][$theta_k eq sqrt(frac(k!, overline(X^k))) \ theta eq 1/overline(X)$][Равномерное][$cases(frac(1, b - a) space.quad &a lt.eq x lt.eq b, 0 space.quad &x lt a " или " x gt b)$][$frac(a + b, 2)$][$frac((b - a)^2, 12)$][$a eq 2 overline(X) - b$][Пуассона][$frac(lambda^k e^(-lambda), k!)$][$lambda$][$lambda$][$lambda eq overline(X)$][Биномиальное][$binom(n, k) p^k (1 - p)^(n - k)$][$n p$][$n p (1 - p)$][$p eq frac(overline(X), n) \ theta eq 1 - frac(S^2, overline(x)) \ theta eq frac(overline(X), m)$][Нормальное][][$a$][$sigma^2$][$a eq overline(X)$][Геометрическое][$(1 - p)^(k - 1) p$][$1/p$][$frac(1 - p, p^2)$][$p eq frac(1, overline(X)) \ theta_1 eq frac(1, overline(X)) \ theta_2 eq frac(-1 + sqrt(1 + 8 overline(X^2)), 2 overline(X^2)) \ theta eq frac(1, overline(X))$], + supplement: [Табл.], + caption: [Виды распределений и их параметры.] + ) +] + +#align(center)[= Построение гистограммы] + +```py +import numpy as np +import matplotlib.pyplot as plt + +def main() -> None: + data = np.array([v for v in open("data.csv", 'r')]) + + plt.figure() + + plt.hist(data, bins = 10, edgecolor='black', justify=True) + + plt.show() # показать гистограмму + + a, b = np.histogram(data, bins=10) + print(a) # количество элементов в каждом промежутке + + +if __name__ == "__main__": + main() + +``` + +#align(center)[= Нахождение параметров выборки] + +```py +import numpy as np + +def main() -> None: + + data = np.array([v for v in open("data.csv", 'r')]) + + print(data.mean()) + print(data.var(ddof=1)) # поделенное на (n - 1) (несмещенное) + print(data.var(ddof=0)) # смещенное + +if __name__ == "__main__": + main() +``` + + +#align(center)[= Нормальное/Гауссово распределение] + +```py +np.random.normal(loc, scale, size) + +# loc - (mean) where the peak of the bell exists. +# scale - (standard deviation) how flat the graph distribution should be. +# size - the shape of the returned array. +``` + +#align(center)[= Биномиальное распределение] + +```py +np.random.binomial(n, p, size) + +# n - number of trials. +# p - probability of occurrence of each trial (e.g. for toss of a coin 0.5 each). +# size - the shape of the returned array. +``` + +#align(center)[= Распределение Пуассона] + +```py +np.random.poisson(lam, size) + +# lam - rate or known number of occurrences e.g. 2 for above problem. +# size - the shape of the returned array. +``` + +#align(center)[= Равномерное распределение] + +```py +np.random.uniform(low, high, size) + +# low - lower bound - default 0.0 +# high - upper bound - default 1.0 +# size - The shape of the returned array +``` + +#align(center)[= Экспоненциальное/показательное распределение] + +```py +np.random.exponential(scale, size) + +# scale - inverse of rate ( see lam in poisson distribution ) defaults to 1.0 +# size - The shape of the returned array +``` + +#align(center)[= Геометрическое распределение] + +```py +np.random.geometric(p, size) + +# p (float): Probability of success (0 < p ≤ 1) +# size (int or tuple, optional): output shape. if None, returns a single value. +``` +