MathLiveChebyshev's inequality
Bounds the probability that a random variable deviates from its mean by at least a given amount, using only its variance. It is used when the full distribution is unknown but the mean and variance are finite.
\Pr(|X-\mathrm{E}[X]| \geq a) \leq \frac{\mathrm{Var}[X]}{a^2}What the symbols mean
| random variable with finite expected value and variance | |
| expected value (mean) of X | |
| variance of X | |
| positive threshold for the deviation from the mean |
About this formula
- FieldStatistics
- TopicProbability inequalities
- LevelUniversity
- Also calledBienaymé–Chebyshev inequality, Chebyshev inequality bound on deviation from mean, probability random variable far from mean, variance bound tail probability, Chebyshev bound, deviation from expected value inequality
- SourceWikidata Q249514
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “chebyshev's inequality”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.