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The distribution of the square of the minimum of two normal random variables

  1. Jul 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Let X and Y be i.i.d normal random variables with mean 0 and variance (that is, N(0,1)). If Z=min(X,Y). Prove that the square of Z is a Gamma distribution and identify the parameters.

    My problem is that the cdf of a normal random variable has no exact form. I need the cdf of normal random variale so that i can evaluate min(X,Y). If you can offer me advice on how i can solve this without the need of the cdf, it would be great


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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