146 lines
4.3 KiB
Typst
146 lines
4.3 KiB
Typst
#show math.equation: set text(size: 12pt, weight: "light", top-edge: "ascender", bottom-edge: "descender")
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#set page(
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paper: "a4",
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margin: (x: 1.8cm, y: 1.5cm),
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)
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#set text(
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font: "New Computer Modern",
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size: 12pt,
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lang: "ru",
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weight: "light"
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)
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#set par(
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// first-line-indent: (
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// amount: 1.5em,
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// all: true
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//),
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justify: true,
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leading: 0.52em,
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)
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#show raw.where(block: false): box.with(
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fill: luma(240),
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inset: (x: 3pt, y: 0pt),
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outset: (y: 3pt),
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radius: 2pt,
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)
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#show raw.where(block: true): block.with(
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fill: luma(240),
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inset: 10pt,
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radius: 4pt,
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)
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#align(center)[= Распределения]
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#align(center)[
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#figure(
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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][$(1 - p)^(k - 1) p$][$1/p$][$frac(1 - p, p^2)$][$p eq frac(1, overline(X)) \ theta_1 eq frac(1, overline(X)) \ theta_2 eq frac(-1 + sqrt(1 + 8 overline(X^2)), 2 overline(X^2)) \ theta eq frac(1, overline(X))$],
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supplement: [Табл.],
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caption: [Виды распределений и их параметры.]
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)
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]
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#align(center)[= Построение гистограммы]
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```py
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import numpy as np
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import matplotlib.pyplot as plt
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def main() -> None:
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data = np.array([v for v in open("data.csv", 'r')])
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plt.figure()
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plt.hist(data, bins = 10, edgecolor='black', justify=True)
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plt.show() # показать гистограмму
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a, b = np.histogram(data, bins=10)
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print(a) # количество элементов в каждом промежутке
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if __name__ == "__main__":
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main()
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```
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#align(center)[= Нахождение параметров выборки]
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```py
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import numpy as np
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def main() -> None:
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data = np.array([v for v in open("data.csv", 'r')])
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print(data.mean())
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print(data.var(ddof=1)) # поделенное на (n - 1) (несмещенное)
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print(data.var(ddof=0)) # смещенное
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if __name__ == "__main__":
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main()
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```
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#align(center)[= Нормальное/Гауссово распределение]
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```py
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np.random.normal(loc, scale, size)
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# loc - (mean) where the peak of the bell exists.
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# scale - (standard deviation) how flat the graph distribution should be.
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# size - the shape of the returned array.
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```
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#align(center)[= Биномиальное распределение]
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```py
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np.random.binomial(n, p, size)
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# n - number of trials.
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# p - probability of occurrence of each trial (e.g. for toss of a coin 0.5 each).
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# size - the shape of the returned array.
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```
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#align(center)[= Распределение Пуассона]
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```py
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np.random.poisson(lam, size)
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# lam - rate or known number of occurrences e.g. 2 for above problem.
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# size - the shape of the returned array.
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```
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#align(center)[= Равномерное распределение]
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```py
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np.random.uniform(low, high, size)
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# low - lower bound - default 0.0
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# high - upper bound - default 1.0
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# size - The shape of the returned array
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```
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#align(center)[= Экспоненциальное/показательное распределение]
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```py
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np.random.exponential(scale, size)
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# scale - inverse of rate ( see lam in poisson distribution ) defaults to 1.0
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# size - The shape of the returned array
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```
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#align(center)[= Геометрическое распределение]
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```py
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np.random.geometric(p, size)
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# p (float): Probability of success (0 < p ≤ 1)
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# size (int or tuple, optional): output shape. if None, returns a single value.
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```
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