Random variables having a distribution

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Reference no: EM131851866

Let X₁, ..., X_n be i.i.d. random variables having a distribution P ∈ P, where P is the family of distributions on R having continuous c.d.f.'s. Let T = (X₍₁₎, ..., X_(n)) be the vector of order statistics. Show that, given T, the conditional distribution of X = (X₁, ..., X_n) is a discrete distribution putting probability 1/n! on each of the n! points (X_i1 , ..., X_in ) ∈ R_n, where {i₁, ..., i_n} is a permutation of {1, ..., n}; hence, T is sufficient for P ∈ P.

Reference no: EM131851866

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