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Markov's Inequality Tail-Probability Bound Calculator

P(X ≥ a) ≤ μ / a (X ≥ 0, a > 0).

Compute Markov's inequality upper bound on the right-tail probability of a non-negative random variable X with mean μ: P(X ≥ a) ≤ μ / a (a > 0). Distribution-free; usually loose but always valid. Useful as a starting point or sanity-check bound when only the mean is known.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(X ≥ a) ≤ μ / a.

In depth

Compute Markov's inequality upper bound on the right-tail probability of a non-negative random variable X with mean μ: P(X ≥ a) ≤ μ / a (a > 0). Distribution-free; usually loose but always valid. Useful as a starting point or sanity-check bound when only the mean is known.