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

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

    Of course I will start from the density function of $\displaystyle Y_{(k)} $. Then I will set up the integral, from $\displaystyle a$ to $\displaystyle b$, of $\displaystyle y $ times this density function. But how can I solve it?
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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 $\displaystyle Y_1 ,...., Y_n$ be a random sample from an uniform distribution $\displaystyle U[a,b]$, both positives. Let $\displaystyle Y_{(k)} $ be the kth order statistic (that is the k-th smallest value extracted from that sample) from a sample of $\displaystyle n$ observations.

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

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