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Thread: A question in order statistics of continuous type distribution

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    A question in order statistics of continuous type distribution




    Let X1,X2, be a sequence of random variables from a continuous type distribution and m and n be two integers such that m<n, and 2≤n−m.

    How can I show the probability that the third-order statistic of X1,,Xm is equal to the fifth-order statistic of X1,,Xn is 6⋅(n−5 m−3)(n m)?

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    Re: A question in order statistics of continuous type distribution


    Rewrite the probability in terms of ranks of variables X1, ..., Xn (these ranks would range from 1 to n).

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