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Math Help - how to prove this pdf relation?

  1. #1
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    how to prove this pdf relation?

    Given iid continuous random variables X_1, X_2,...,X_n, let Y=g(X_1,...,X_n) be some well-behaved function (e.g., sum) of these r.v.'s and f be the joint pdf of X_1, ...,X_n,Y. Do we have f(x_1,...,x_n,y)=f(x_1,...,x_n) if y=g(x_1,...,x_n) and f(x_1,...,x_n,y)=0 if y\neq(x_1,...,x_n)? If so, how to prove? This statement is obviously true for pmf, but I have no idea for pdf.
    Thanks a lot!
    Last edited by zzzhhh; June 5th 2012 at 11:44 PM.
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