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  "body": "\n## Definition\n\nLet $(\\Omega, \\mathcal{F}, P)$ be a probability space and let $(A_i)_{i \\in I}$ be a family of events.\nThe family is pairwise independent if $A_i$ and $A_j$ are [[independent|0P0MZ4X682]] for all $i, j \\in I$ with $i \\ne j$, that is, $P(A_i \\cap A_j) = P(A_i) \\, P(A_j)$.\n\n## Remarks\n\n[[Mutual independence|0GCVEV6BJA]] implies pairwise independence, but the converse is false. The node [[pairwise independent events that are not mutually independent|0AR4B3K5QD]] gives an example.\nThe same definition applies to random variables: any two of them are independent.\nPairwise independence is enough for some results.\nExamples are the formula for the variance of a sum and the weak law of large numbers with finite variance.\n\n## Explanations\n\n### L1 human\n\nPairwise independence checks the events two at a time.\nIt can happen that each pair of events is independent, but a group of three events is not.\n",
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