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definetti.pdf

colorado.edu · 2,504 words · saved by 1 readers

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Exchangeability and deFinetti’s Theorem Definition: The random variables X1 , X2 , . . . , Xn are said to be exchangeable if the distribution of the random vector (X1 , X2 , . . . , Xn ) is the same as that of (Xπ1 , Xπ2 , . . . , Xπn ) for any permuta- tion (π1 , π2 , . . . , πn ) of the indices {1, 2, . . . , n}. We write d (X1 , X2 , . . . , Xn ) = (Xπ1 , Xπ2 , . . . , Xπn ). This means that the pdf or cdf for (X1 , X2 , . . . , Xn ) must be the same as that for (Xπ1 , Xπ2 , . . . , Xπn ).…

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