Uniform Random Sampling in Python
Uniform random sampling is a fundamental technique in simulations and probabilistic modeling. You use it to generate random numbers that are equally likely to fall anywhere within a specified interval, most often between 0 and 1. This approach is essential because many simulation methods, including Monte Carlo techniques, rely on the ability to produce random samples that are unbiased and uniformly distributed. By ensuring that every number in the interval has an equal chance of being selected, you can model randomness accurately and build more reliable simulations.
123456789101112131415161718192021222324252627import numpy as np import matplotlib.pyplot as plt # Generate an array of 1000 uniform random numbers between 0 and 1 uniform_01 = np.random.uniform(0, 1, 1000) # Generate an array of 1000 uniform random numbers between 10 and 20 uniform_10_20 = np.random.uniform(10, 20, 1000) plt.figure(figsize=(12, 5)) # Plot for [0, 1] interval plt.subplot(1, 2, 1) plt.hist(uniform_01, bins=30, color='skyblue', edgecolor='black') plt.title('Uniform Distribution [0, 1]') plt.xlabel('Value') plt.ylabel('Frequency') # Plot for [10, 20] interval plt.subplot(1, 2, 2) plt.hist(uniform_10_20, bins=30, color='salmon', edgecolor='black') plt.title('Uniform Distribution [10, 20]') plt.xlabel('Value') plt.ylabel('Frequency') plt.tight_layout() plt.show()
In the code above, you use the numpy library's random.uniform function to generate random numbers. This function allows you to specify the lower and upper bounds of the interval from which the numbers are drawn. By default, the uniform distribution is continuous and every number within the interval has the same probability of being selected. When you generate a single value, you get one random sample; when you pass a size argument, you receive an array of independent samples, all drawn from the same uniform distribution. This property makes uniform random sampling especially powerful for simulating random events, initializing random variables, or serving as the foundation for more complex probabilistic models.
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Uniform random sampling is a fundamental technique in simulations and probabilistic modeling. You use it to generate random numbers that are equally likely to fall anywhere within a specified interval, most often between 0 and 1. This approach is essential because many simulation methods, including Monte Carlo techniques, rely on the ability to produce random samples that are unbiased and uniformly distributed. By ensuring that every number in the interval has an equal chance of being selected, you can model randomness accurately and build more reliable simulations.
123456789101112131415161718192021222324252627import numpy as np import matplotlib.pyplot as plt # Generate an array of 1000 uniform random numbers between 0 and 1 uniform_01 = np.random.uniform(0, 1, 1000) # Generate an array of 1000 uniform random numbers between 10 and 20 uniform_10_20 = np.random.uniform(10, 20, 1000) plt.figure(figsize=(12, 5)) # Plot for [0, 1] interval plt.subplot(1, 2, 1) plt.hist(uniform_01, bins=30, color='skyblue', edgecolor='black') plt.title('Uniform Distribution [0, 1]') plt.xlabel('Value') plt.ylabel('Frequency') # Plot for [10, 20] interval plt.subplot(1, 2, 2) plt.hist(uniform_10_20, bins=30, color='salmon', edgecolor='black') plt.title('Uniform Distribution [10, 20]') plt.xlabel('Value') plt.ylabel('Frequency') plt.tight_layout() plt.show()
In the code above, you use the numpy library's random.uniform function to generate random numbers. This function allows you to specify the lower and upper bounds of the interval from which the numbers are drawn. By default, the uniform distribution is continuous and every number within the interval has the same probability of being selected. When you generate a single value, you get one random sample; when you pass a size argument, you receive an array of independent samples, all drawn from the same uniform distribution. This property makes uniform random sampling especially powerful for simulating random events, initializing random variables, or serving as the foundation for more complex probabilistic models.
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