 Second moment method

For a nonnegative random variable $N$, Chebyshev's inequality givesHence $\mathrm{var}(N)/(\mathbb{E}N{)}^2\to 0$ implies that $N>0$ with probability tending to one.

The second moment method is a technique in probability theory and combinatorics often used to prove the existence of certain properties of random structures, typically applied in probabilistic combinatorics and random graph theory. This method leverages the second moment of a random variable to provide bounds on the probability that the variable takes on a certain value or exceeds a certain threshold.