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    Probability

    Let x and y be uniformly distributed independent random variables over [0,1]. What is the probability the distance between x and y is less than 1/2?
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  2. #2
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    This can be a geometry problem, since the distributions are uniform.

    You need p(|x-y|  < \frac{1}{2})

    For x > y, we have x - y < \frac{1}{2} or y > x - \frac{1}{2}

    This cuts off a corner.

    You do x < y to cut off the other corner. You're almost done.
    Last edited by mr fantastic; June 19th 2010 at 10:07 PM. Reason: Fixed a typo.
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    Quote Originally Posted by mathman88 View Post
    Let x and y be uniformly distributed independent random variables over [0,1]. What is the probability the distance between x and y is less than 1/2?
    Unit square:


    Area of shaded region = 3/4.
    Attached Thumbnails Attached Thumbnails Probability-rand2vars.png  
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