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Sum of squared uniform random variables

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    If X and Y are independent uniformly distributed random variables between 0 and 1, what is the probability that X^2+Y^2 is less than or equal to one.

    2. Relevant equations
    P(Z<1) = P(X^2+Y^2<1)

    For z between 0 and 1, P(X^2<z) = P(X < √z) = √z

    3. The attempt at a solution
    I'm a tad lost- I assume what you'd be looking for is the probability that Y^2 is less than or equal 1-X^2, or rather that Y is less or equal to √(1-X^2). Is that all there is to it?
     
  2. jcsd
  3. Dec 8, 2011 #2
    You have to remember something really important about variables between 1 and zero. Here it is:

    if xε[0,1[ then x^2<x and √x> x I think that should help you a bit
     
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