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Probability Inequalities



Markov Inequality
Bound tail probabilities using only the expected value. P(X ≥ a) ≤ E[X] / a
Chebyshev Inequality
Bound deviations from the mean using variance. P(|X - μ| ≥ a) ≤ σ² / a²





Interactive Probability Inequality Tools

Explore fundamental probability inequalities through interactive visualizations. See how these bounds work across different distributions and parameter settings.



What are Probability Inequalities?

Probability inequalities provide upper bounds on the probability of events without requiring full knowledge of the distribution. They are fundamental tools in probability theory and statistics.
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Why Use Inequalities?

When we know limited information about a random variable (like its mean or variance), inequalities let us bound probabilities and make guarantees about tail behavior.
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Applications

Probability inequalities are used in statistical inference, machine learning convergence proofs, algorithm analysis, and risk assessment across various fields.
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