Problem 3

binomial_coeffs.py

@@ -0,0 +1,24 @@
+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
+
+
+N = 10
+print("N:", N)
+
+coeffs = pascal(N)
+print("coefficients:", coeffs)
+
+normalized_coeffs = coeffs / 2 ** N
+print("normalized coefficients:", normalized_coeffs)
+
+expect_x = np.sum(normalized_coeffs) / len(normalized_coeffs)
+expect_x_sqrd = np.sum(normalized_coeffs ** 2) / len(normalized_coeffs)
+std = np.sqrt(expect_x_sqrd - expect_x ** 2)
+print("std", std)