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import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import poisson

# Mean for the Poisson distribution
mu = 1.64706

# Values of k (number of cases)
k_values = np.arange(0, 10)

# Calculate the probabilities
probabilities = poisson.pmf(k_values, mu)

# Create a bar plot
plt.bar(k_values, probabilities, color='blue', alpha=0.7, align='center')
plt.title('Poisson Distribution: $\mu=1.64706$')
plt.xlabel('Number of Cases ($k$)')
plt.ylabel('Probability')
plt.show()