Oppiskele Visualizing Probability Distributions

Osio 1. Luku 10

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Visualizing probability distributions helps you gain a deeper understanding of how random variables behave. In Python, the matplotlib library is a powerful tool for creating such visualizations. You can use it to plot both probability mass functions (PMFs) for discrete distributions and probability density functions (PDFs) for continuous distributions.

To visualize a PMF, you typically use bar plots to represent the probabilities associated with each possible outcome. For continuous distributions, you plot the PDF as a smooth curve, showing how probability is distributed over a range of values. These plots allow you to quickly see where outcomes are most likely, spot symmetry or skewness, and compare different distributions.

When working with discrete distributions like the binomial, you often want to show the probability of getting a certain number of successes in a fixed number of trials. For continuous distributions like the normal distribution, you want to show how likely values are to fall within a certain interval. Using matplotlib, you can create clear, informative plots to support your analysis of probability problems.


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import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import binom, norm

# Plotting the Binomial Distribution (Discrete)
n, p = 10, 0.5  # 10 trials, probability of success 0.5
x_binom = np.arange(0, n+1)
pmf_binom = binom.pmf(x_binom, n, p)

plt.figure(figsize=(8, 4))
plt.bar(x_binom, pmf_binom, color='skyblue', edgecolor='black')
plt.title('Binomial Distribution PMF (n=10, p=0.5)')
plt.xlabel('Number of Successes')
plt.ylabel('Probability')
plt.show()

# Plotting the Normal Distribution (Continuous)
mu, sigma = 0, 1  # mean and standard deviation
x_norm = np.linspace(-4, 4, 1000)
pdf_norm = norm.pdf(x_norm, mu, sigma)

plt.figure(figsize=(8, 4))
plt.plot(x_norm, pdf_norm, color='darkorange')
plt.title('Normal Distribution PDF (μ=0, σ=1)')
plt.xlabel('Value')
plt.ylabel('Density')
plt.grid(True)
plt.show()

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Osio 1. Luku 10

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