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Predicting the value of Pi for differnet number of randomly generated samples. The samples are uniformly generated.

Author: HummdG

predicting_pi/predicting_pi.py

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+import mpmath
+import matplotlib.pyplot as plt
+
+def estimate_pi(num_samples):
+    points_inside_circle = 0
+
+    for _ in range(num_samples):
+        x = mpmath.rand()
+        y = mpmath.rand()
+
+        distance = x**2 + y**2
+
+        if distance <= 1:
+            points_inside_circle += 1
+
+    pi_estimate = mpmath.mpf(4 * points_inside_circle) / mpmath.mpf(num_samples)
+    return pi_estimate
+
+# Set the precision to 30 decimal places
+mpmath.mp.dps = 30
+
+# List to store the estimated values of pi for different sample sizes
+pi_estimates = []
+
+# List of different sample sizes
+sample_sizes = [10, 100, 1000, 10000, 100000, 1000000]
+
+# Estimating pi for each sample size
+for num_samples in sample_sizes:
+    pi_approximation = estimate_pi(num_samples)
+    pi_estimates.append(pi_approximation)
+
+# Plotting the results
+plt.plot(sample_sizes, pi_estimates, marker='o')
+plt.xscale('log')  # Use a logarithmic scale for the x-axis
+plt.axhline(y=mpmath.pi, color='r', linestyle='--', label='True value of pi')
+plt.xlabel('Number of Samples')
+plt.ylabel('Approximation of pi')
+plt.title('Monte Carlo Estimation of Pi for Varying # of Samples')
+plt.legend()
+plt.show()