Law of Large Numbers Python
import numpy as np import matplotlib.pyplot as plt Example 1 Coin Flips (Bernoulli Distribution)
#If we repeat the coin flip multiple times, the sum of these Bernoulli trials follows a
#Binomial distribution. However, when looking at a single flip, it’s simply a Bernoulli distribution
np.random.seed(15) # For reproducibility # Number of trials (coin flips) n_trials = 10000 # Simulate coin flips coin_flips = np.random.randint(0, 2, size=n_trials) print(coin_flips) 
# Calculate cumulative mean cumulative_mean = np.cumsum(coin_flips) / (np.arange(1, n_trials + 1)) print(cumulative_mean) 
plt.figure(figsize=(10, 6)) plt.plot(cumulative_mean, label='Cumulative Mean') plt.axhline(y=0.5, color='r', linestyle='--', label='Expected Value (0.5)') plt.xlabel('Number of Trials') plt.ylabel('Cumulative Mean') plt.title('Law of Large Numbers: Coin Flip Example') plt.legend() plt.show() 
Example 2 Data Science Salaries (Normal Distribution)
# Number of samples (salaries) n_samples = 10000 # Parameters of the salary distribution mu = 120000 # Mean salary sigma = 30000 # Standard deviation # Generate random samples of salaries salaries = np.random.normal(mu, sigma, n_samples) print(salaries) 
# Calculate cumulative mean cumulative_mean_salaries = np.cumsum(salaries) / (np.arange(1, n_samples + 1)) print(cumulative_mean_salaries) 
plt.figure(figsize=(10, 6)) plt.plot(cumulative_mean_salaries, label='Cumulative Mean Salary') plt.axhline(y=mu, color='r', linestyle='--', label=f'Expected Mean Salary (${mu})') plt.xlabel('Number of Samples') plt.ylabel('Cumulative Mean Salary') plt.title('Law of Large Numbers: U.S. Data Science Salaries') plt.legend() plt.show() 
