Problem 1.1

1.1.py

@@ -0,0 +1,26 @@
+import numpy as np
+
+ages = np.array([14, 15, 16, 16, 16, 22, 22, 24, 24, 25, 25, 25, 25, 25])
+
+# a
+
+expect_j_sqrd = np.sum(ages ** 2) / ages.size
+print("<j^2>:", expect_j_sqrd)
+
+expect_j = np.sum(ages) / ages.size
+print("<j>^2:", expect_j ** 2)
+
+# b
+
+unique_ages = np.unique(ages)
+unique_delta_js = unique_ages - expect_j
+print("delta js:", [(unique_ages[i], unique_delta_js[i]) for i in range(len(unique_ages))])
+
+delta_js = ages - expect_j
+std_eq11 = np.sqrt(np.sum(delta_js ** 2) / delta_js.size)
+print("std eq. 1.11:", std_eq11)
+
+# c
+
+std_eq12 = np.sqrt(expect_j_sqrd - expect_j ** 2)
+print("std eq. 1.12:", std_eq12)

scratch.py

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+import numpy as np
+import math as m
+
+
+def pascal(n: int) -> np.ndarray:
+    p = np.zeros(n + 1)
+    for i in range(n + 1):
+        p[i] = m.factorial(n) / (m.factorial(i) * m.factorial(n - i))
+    return p
+
+
+def normalized_pascal(n: int) -> np.ndarray:
+    return pascal(n) / 2 ** n
+
+
+N = 10
+heads = np.arange(N + 1)
+print("heads:", heads)
+
+print("pascal:", normalized_pascal(N))