Problem 1.1
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1.1.py
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26
1.1.py
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import numpy as np
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ages = np.array([14, 15, 16, 16, 16, 22, 22, 24, 24, 25, 25, 25, 25, 25])
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# a
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expect_j_sqrd = np.sum(ages ** 2) / ages.size
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print("<j^2>:", expect_j_sqrd)
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expect_j = np.sum(ages) / ages.size
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print("<j>^2:", expect_j ** 2)
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# b
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unique_ages = np.unique(ages)
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unique_delta_js = unique_ages - expect_j
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print("delta js:", [(unique_ages[i], unique_delta_js[i]) for i in range(len(unique_ages))])
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delta_js = ages - expect_j
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std_eq11 = np.sqrt(np.sum(delta_js ** 2) / delta_js.size)
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print("std eq. 1.11:", std_eq11)
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# c
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std_eq12 = np.sqrt(expect_j_sqrd - expect_j ** 2)
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print("std eq. 1.12:", std_eq12)
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scratch.py
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scratch.py
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import numpy as np
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import math as m
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def pascal(n: int) -> np.ndarray:
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p = np.zeros(n + 1)
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for i in range(n + 1):
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p[i] = m.factorial(n) / (m.factorial(i) * m.factorial(n - i))
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return p
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def normalized_pascal(n: int) -> np.ndarray:
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return pascal(n) / 2 ** n
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N = 10
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heads = np.arange(N + 1)
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print("heads:", heads)
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print("pascal:", normalized_pascal(N))
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