# pr.likelihood – How can I show Chebyshev’s sum inequality with probabilistic strategies? Answer

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pr.likelihood – How can I show Chebyshev’s sum inequality with probabilistic strategies?

I’d love to show Chebyshev’s sum inequality, which states that:

If $$a_1geq a_2geq cdots geq a_n$$ and $$b_1geq b_2geq cdots geq b_n$$, then
$$frac{1}{n}sum_{okay=1}^n a_kb_kgeq left(frac{1}{n}sum_{okay=1}^n a_kright)left(frac{1}{n}sum_{okay=1}^n b_kright)$$
I’m close with the non-probabilistic proof, however I necessity a probabilistic one.

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