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Math Help - rectangular distribution problem

  1. #1
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    rectangular distribution problem

    Having another problem. Not sure how to even approach this problem. I figure I should be using rectangular distribution somehow.


    Let X and Y denote the lengths of the two sides of a rectangle and let them possess independent rectangular distributions over the interval (0,1).
    Calculate the probability that the length of a diagonal of this rectangle will be less than one.



    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by BklynKid View Post
    Having another problem. Not sure how to even approach this problem. I figure I should be using rectangular distribution somehow.


    Let X and Y denote the lengths of the two sides of a rectangle and let them possess independent rectangular distributions over the interval (0,1).
    Calculate the probability that the length of a diagonal of this rectangle will be less than one.



    Any help would be appreciated.
    The square of the diagonal of the random rectangle is d^2=x^2+y^2, the probability that the diagonal is less than one is: p(x^2+y^2<1), which as x \sim U(0,1) and y \sim U(0,1), is the probability that a random point in the square [0,1]\times [0,1] lies inside the unit circle.

    This probability is equal to the area of the unit circle inside the square, which is a quarter of the area or the unit circle or \pi/4

    RonL
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  3. #3
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    Thanks for the swift reply. To be honest, I don't really understand the reason (I already knew the solution) but perhaps it'll come to me later.

    Again, thank you.
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