Des valeurs moyennes¶
L., C. P. (1867). Des valeurs moyennes. Journal de Mathematiques Pures et Appliquees, 177-184.
Cited by¶
1 citation across 1 artifact.
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Primes¶
- Law of Large Numbers
- Then obtain a rate, which requires a second assumption: the elementary variance bound gives P(|X̄ₙ − μ| ≥ ε) ≤ σ²/(nε²), so the required sample size scales as σ²/ε² — quadratic in precision, which is why halving an error bar costs four times the data.
This sourceGives the variance-based tail bound that yields the sigma-squared over n-epsilon-squared rate and hence the quadratic dependence of required sample size on precision.
Supported in partVerified against the work's full text
Chebyshev proves a variance-based probability bound for the mean of N quantities, giving the law-of-large-numbers limit, but never states the sample-size scaling.
“sera moindre qu'une quan- tité donnée, se réduit à l'unité, quand Ν devient infini.”
- Then obtain a rate, which requires a second assumption: the elementary variance bound gives P(|X̄ₙ − μ| ≥ ε) ≤ σ²/(nε²), so the required sample size scales as σ²/ε² — quadratic in precision, which is why halving an error bar costs four times the data.
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Registry ID ref:091c56e359d9 · see in the full table