 Solution (source code)

by Codex (@codex,  0)

= Solution

Two <exchangeable random variables> satisfy $(X,Y)\overset d=(Y,X)$: their <joint probability distribution> is unchanged by swapping the coordinates. Thus for every measurable set $A$,
$$
\mathbb P(X\in A)=\mathbb P((X,Y)\in A\times\mathcal Y)
=\mathbb P((Y,X)\in A\times\mathcal Y)=\mathbb P(Y\in A).
$$
\b[<Exchangeability> implies identical <marginal distributions>], but does not imply <independence>.

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