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  "body": "\n## Summary\n\nA finite or infinite sequence of [[random variables|0PNRKMRC55]] is exchangeable when its [[joint distribution|0DR81R1F2B]] does not change if finitely many of the variables are permuted.\nEvery sequence of [[independent and identically distributed|00MRN0FARV]] random variables is exchangeable, but exchangeable variables need not be independent.\nExchangeability is the basic symmetry assumption of Bayesian statistics.\nBy [[de Finetti's theorem|W19129PVKQ]], an infinite exchangeable sequence is a mixture of i.i.d. sequences.\n\n## Explanations\n\n### L1 human\n\nExchangeable means that the order of the observations carries no information.\nDraw balls one by one, without replacement, from an urn with $3$ red and $2$ blue balls.\nThe chance that the first ball is red and the second is blue equals the chance that the first is blue and the second is red: both are $\\frac{3}{5} \\cdot \\frac{2}{4} = \\frac{2}{5} \\cdot \\frac{3}{4} = \\frac{3}{10}$.\nThe colours are exchangeable, yet they are not independent, since a red first ball makes a red second ball less likely.\n",
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