When working with probability distributions in Python, it is important to have a clear understanding of the problem at hand and choose the most appropriate solution. In this article, we will explore three different ways to solve a probability distribution of sample proportion question using Python.

Option 1: Using the scipy.stats module

The scipy.stats module provides a wide range of statistical functions and probability distributions. To solve the given question, we can use the binom module from scipy.stats to calculate the probability distribution of a sample proportion.

import scipy.stats as stats

# Define the parameters
n = 100  # Number of trials
p = 0.6  # Probability of success

# Calculate the probability distribution
dist = stats.binom(n, p)

# Print the probability distribution
print(dist.pmf(range(n+1)))

This code snippet defines the number of trials (n) and the probability of success (p). It then uses the binom function from the scipy.stats module to create a probability distribution object. Finally, it prints the probability mass function (pmf) of the distribution for all possible values of the sample proportion.

Option 2: Using the numpy module

The numpy module is a powerful library for numerical computing in Python. We can use numpy to generate a random sample and calculate the sample proportion. By repeating this process multiple times, we can approximate the probability distribution of the sample proportion.

import numpy as np

# Define the parameters
n = 100  # Number of trials
p = 0.6  # Probability of success
num_samples = 10000  # Number of samples

# Generate random samples
samples = np.random.binomial(n, p, num_samples)

# Calculate the sample proportion
proportions = samples / n

# Print the probability distribution
print(np.histogram(proportions, bins=np.linspace(0, 1, 11))[0])

This code snippet uses the numpy module to generate random samples from a binomial distribution with the given parameters. It then calculates the sample proportion by dividing the number of successes by the total number of trials. Finally, it prints the histogram of the sample proportions to approximate the probability distribution.

Option 3: Using the math module

If you prefer a more basic approach, you can use the math module to calculate the probability distribution of a sample proportion. This method involves manually calculating the binomial coefficient and the probability mass function.

import math

# Define the parameters
n = 100  # Number of trials
p = 0.6  # Probability of success

# Calculate the probability distribution
dist = [math.comb(n, k) * (p ** k) * ((1 - p) ** (n - k)) for k in range(n+1)]

# Print the probability distribution
print(dist)

This code snippet uses the math.comb function to calculate the binomial coefficient and manually calculates the probability mass function for all possible values of the sample proportion. Finally, it prints the probability distribution.

After exploring these three options, it is clear that using the scipy.stats module (Option 1) is the most efficient and convenient solution. It provides a simple and straightforward way to calculate the probability distribution of a sample proportion in Python. However, depending on the specific requirements of your problem, the other options may also be suitable.