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Math Help - Uniform distribution.

  1. #1
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    Uniform distribution.

    The following question has got me puzzled so if anyone could give me a start, I would be very grateful:

    Suppose you choose 3 numbers at random that are uniformly distributed on the interval [0,1]. What is the expected value of the maximum of the three numbers?
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  2. #2
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    Quote Originally Posted by buckaroobill View Post
    The following question has got me puzzled so if anyone could give me a start, I would be very grateful:

    Suppose you choose 3 numbers at random that are uniformly distributed on the interval [0,1]. What is the expected value of the maximum of the three numbers?
    prb(max(x_1,x_2,x_3)<a)=prb(x_1<a)prb(x_2<a)prb(x_  3<a)=a^3

    so the pdf of y=max(x_1,x_2,x_3) is:

    p(y)=\left. \frac{d}{da}a^3 \right|_{a=y},\ y \in [0,1],\ \mbox{ and }0 \mbox{ otherwise }

    RonL
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