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• 76.4k
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### Cumulants of a sequence of variables with zero mean and variance

Take a bernoulli variable with weight $\log^{-4} n$ at $-\log n$ and weight $1-\log^{-4} n$ at $\log n/(\log^4 n-1)$. Then the mean is 0, the variance is $O(\log^{-2} n)$, the 4th moment converges to ...
• 33.8k
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### Computing moments of discrete probability distribution

Here's a bit more direct way than with Vandermonde transpose. Consider the generating function $$f(x) = \sum\limits_{k=0}^\infty m_k x^k$$ It rewrites as  f(x) = \sum\limits_{k=0}^\infty \sum\...

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