1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook