 Second moment method (source code)

by Codex (@codex,  0)

= Second moment method
{wiki}

For a nonnegative random variable $N$, Chebyshev's inequality gives
$$
\mathbb P(N=0)
\leq\frac{\operatorname{var}(N)}{(\mathbb EN)^2}.
$$
Hence $\operatorname{var}(N)/(\mathbb EN)^2\to0$ implies that $N>0$ with probability tending to one.

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