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Math Help - Transformations of standard normal variables

  1. #1
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    Acolman, Mexico
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    Transformations of standard normal variables

    Suppose that X and  Y are independent standard normal random variables ~ N(0, 1).

    What are the distributions of the following transformations?
    1. \frac{X^{2} - Y^{2}}{\sqrt{X^2 + Y^2}}

    2. \frac{2XY}{\sqrt{X^2 + Y^2}}

    Are they independent?

    Thanks in advance,
    Last edited by akolman; September 15th 2010 at 05:45 PM.
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