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Marcocapelle (talk | contribs) removed Category:Probability theory; added Category:Statistical randomness using HotCat |
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These equations show the joint distribution or density characterised as a mixture distribution based on the underlying limiting empirical distribution (or a parameter indexing this distribution).
Note that not all finite exchangeable sequences are mixtures of i.i.d. To see this, consider sampling without replacement from a finite set until no elements are left. The resulting sequence is exchangeable, but not a mixture of i.i.d. Indeed, conditioned on all other elements in the sequence, the remaining element is known.
== Covariance and Correlation ==
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