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Sum of Squared RVs

  1. Jul 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Let X,Y be two gaussian random variables that neither have the same variance nor the same mean necessarily, and both may be nonstandard. If I were to construct an RV of the form
    R = √(X2 + Y2), how would this RV be distributed?

    3. The attempt at a solution

    So I've given this a fair amount of thought. At first, I thought it might be distributed as a Rician, but that seems to require that both RVs have the same variance. Eventually I concluded that it might be Chi distributed. However, since I never divide by the standard deviation of either RV (as would be required to construct either a noncentral Chi or a noncentral Chi-Squared), this also fails to work. Does anyone have any ideas for finding the distribution of two RVs combined in this way?
     
  2. jcsd
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