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Math Help - Finding the Expected Value of the Maximum from a Sample w/ a Continuous Distribution

  1. #1
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    Finding the Expected Value of the Maximum from a Sample w/ a Continuous Distribution

    Hello,

    How would you go about solving this question? This is the problem presented to me:

    Suppose that X1,...,Xn form a random sample of size n from a continuous distribution with the following p.d.f.:

    f(x) = 2x, for 0<x<1
    0 otherwise

    Let Yn = max(X1,...Xn). Evaluate E(Yn).

    Thanks for any help.
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  2. #2
    MHF Contributor
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    Re: Finding the Expected Value of the Maximum from a Sample w/ a Continuous Distribut

    Hey piazzaj.

    Hint: Take a look at the order statistic distribution for the maximum. If you want to derive the maximum you should look at how they do it with order statistics and follow the logic of the derivation. Either way, this is what you are looking for.

    Also intuitively you expect your maximum to tend to 1 (since that is the highest value of possible outcomes) as you get a higher sample size.
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