Finish theory for exercise 2

src/2026-01-30/gen_correlated_data.py

@@ -0,0 +1,38 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from numpy.typing import NDArray
+import argparse
+
+
+def twodim_array_to_pgfplots_table_string(a: NDArray):
+    return (
+        " \\\\\n".join([" ".join([str(vali) for vali in val]) for val in a]) + "\\\\\n"
+    )
+
+
+def main():
+    # Parse command line arguments
+
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--correlation", "-c", type=np.float32, required=True)
+    parser.add_argument("-N", type=np.int32, required=True)
+    parser.add_argument("--plot", "-p", action="store_true")
+
+    args = parser.parse_args()
+
+    # Generate & plot data
+
+    means = np.array([0, 0])
+    cov = np.array([[1, args.correlation], [args.correlation, 1]])
+
+    x = np.random.multivariate_normal(means, cov, size=args.N)
+
+    print(twodim_array_to_pgfplots_table_string(x))
+
+    if args.plot:
+        plt.scatter(x[:, 0], x[:, 1])
+        plt.show()
+
+
+if __name__ == "__main__":
+    main()

src/2026-01-30/gen_histogram.py

@@ -0,0 +1,40 @@
+import argparse
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.special import binom
+
+
+def array_to_pgfplots_table_string(a):
+    return " ".join([f"({k}, {val})" for (k, val) in enumerate(a)]) + f" ({len(a)}, 0)"
+
+
+def P_binom(N, p, k):
+    return binom(N, k) * p**k * (1 - p) ** (N - k)
+
+
+def main():
+    # Parse command line arguments
+
+    parser = argparse.ArgumentParser()
+    parser.add_argument("-N", type=np.int32, required=True)
+    parser.add_argument("-p", type=np.float32, required=True)
+    parser.add_argument("--show", "-s", action="store_true")
+
+    args = parser.parse_args()
+
+    # Generate and show data
+
+    N = args.N
+    p = args.p
+
+    bars = np.array([P_binom(N, p, k) for k in range(N + 1)])
+
+    print(array_to_pgfplots_table_string(bars))
+
+    if args.show:
+        plt.stem(bars)
+        plt.show()
+
+
+if __name__ == "__main__":
+    main()