Serie 01

Serie01/aufg1.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+a = np.array([0, 1, 2, 3, 4, 5, 6])
+h = np.array([83, 25, 28, 18, 12, 10, 2])
+
+n = np.sum(h)
+
+pmf = h / n
+
+H_abs = h.cumsum()
+F_rel = pmf.cumsum()
+
+plt.figure()
+plt.bar(a, h)
+plt.title('Relative Häufigkeit (PMF)')
+plt.xlabel('Anzahl der Defekte')
+plt.ylabel('Absolute Häufigkeit')
+plt.xticks(a)
+plt.tight_layout()
+
+plt.figure()
+plt.bar(a, pmf)
+plt.title('Relative Häufigkeit (PMF)')
+plt.xlabel('Anzahl der Defekte')
+plt.ylabel('Relative Häufigkeit')
+plt.xticks(a)
+plt.tight_layout()
+
+plt.figure()
+plt.step(a, H_abs, where="post")
+plt.title("Absolute Verteilungsfunktion (CDF)")
+plt.xlabel("a_i")
+plt.ylabel("H_i = Σ h_i")
+plt.xticks(a)
+plt.tight_layout()
+
+# 4) CDF relativa (right-continuous)
+plt.figure()
+plt.step(a, F_rel, where="post")
+plt.title("Relative Verteilungsfunktion (CDF)")
+plt.xlabel("a_i")
+plt.ylabel("F_i = Σ P(X=a_i)")
+plt.xticks(a)
+plt.ylim(0, 1.05)
+plt.tight_layout()
+
+plt.show()

Serie01/aufg10.py

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+
+
+x = [2.1, 2.4, 2.8, 3.1, 4.2, 4.9, 5.1, 6.0, 6.4, 7.3,
+     10.8, 12.5, 13.0, 13.7, 14.8, 17.6, 19.6, 23.0, 25.0, 35.2, 39.6]
+
+#median
+n = len(x)
+x_sorted = sorted(x)
+if n % 2 == 1:
+    median = x_sorted[n // 2]
+else:
+    median = (x_sorted[n // 2 - 1] + x_sorted[n // 2]) / 2
+
+print("median"+str(median))
+
+#mean
+mean = sum(x) / n
+print("Mittelwert"+str(mean))
+
+#standard deviation
+variance = sum((xi - mean) ** 2 for xi in x) / n
+std_dev = variance ** 0.5
+print("Standardabweichung"+str(std_dev))
+
+
+#korrigierte Standardabweichung
+corrected_variance = sum((xi - mean) ** 2 for xi in x)
+corrected_std_dev = (corrected_variance / (n - 1)) ** 0.5
+
+print("korrigierte Standardabweichung"+str(corrected_std_dev))
+

Serie01/aufg2.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+d = np.array([1,0,1,1,2,1,0,0,2,1,1,1,3,0,2,2,1,0,2,3,1,1,2,1,1])
+x, h = np.unique(d, return_counts=True)
+fi = h / h.sum()
+Hi = h.cumsum()
+Fi = fi.cumsum()
+
+fig, ax = plt.subplots(2, 1, sharex=True, figsize=(6,6))
+ax[0].bar(x, h, width=0.2)
+ax[0].set_title("Geschwister")
+ax[0].set_ylabel("Absolute Häufigkeit")
+ax[1].bar(x, fi, width=0.2)
+ax[1].set_xlabel("Anzahl Geschwister")
+ax[1].set_ylabel("Relative Häufigkeit")
+fig.tight_layout()
+
+fig2, ax2 = plt.subplots(2, 1, sharex=True, figsize=(6,6))
+ax2[0].step(np.r_[x[0], x], np.r_[0, Hi], where="post")
+ax2[0].set_title("Geschwister")
+ax2[0].set_ylabel("Abs. Summenhäufigkeit")
+ax2[1].step(np.r_[x[0], x], np.r_[0, Fi], where="post")
+ax2[1].set_xlabel("Anzahl Geschwister")
+ax2[1].set_ylabel("Rel. Summenhäufigkeit")
+fig2.tight_layout()
+
+plt.show()

Serie01/aufg8.py

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+import numpy as np
+
+R = np.array([720, 740, 760, 780, 800, 820])
+A = np.array([19, 24, 26, 27, 10, 5])
+B = np.array([4, 8, 52, 40, 32, 24])
+
+def qval(edges, counts, x):
+    cdf = np.cumsum(counts) / counts.sum()
+    i = np.searchsorted(edges, x)
+    if i == 0: return 0.0
+    if i >= len(edges): return 1.0
+    w = edges[1] - edges[0]
+    return cdf[i-1] + (x - edges[i-1]) / w * (cdf[i] - cdf[i-1])
+
+qa = qval(R, A, 730)
+qb = qval(R, B, 750)
+
+print(qa)
+print(qb)