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Math Help - Uniform distribution between (a,b): expected value of kth order statistic

  1. #1
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    Uniform distribution between (a,b): expected value of kth order statistic

    Hello. Please help me understand how to solve this problem.

    Let Y_1 ,...., Y_n be a random sample from an uniform distribution U[a,b], both positives. Let Y_{(k)} be the kth order statistic (that is the k-th smallest value extracted from that sample) from a sample of n observations.

    Find the expected value of Y_{(k)} .

    Of course I will start from the density function of Y_{(k)} . Then I will set up the integral, from a to b, of y times this density function. But how can I solve it?
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  2. #2
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    Re: Uniform distribution between (a,b): expected value of kth order statistic

    Quote Originally Posted by Riccardo View Post
    Hello. Please help me understand how to solve this problem.

    Let Y_1 ,...., Y_n be a random sample from an uniform distribution U[a,b], both positives. Let Y_{(k)} be the kth order statistic (that is the k-th smallest value extracted from that sample) from a sample of n observations.

    Find the expected value of Y_{(k)} .

    Of course I will start from the density function of Y_{(k)} . Then I will set up the integral, from a to b, of y times this density function. But how can I solve it?
    This might help.
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