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Maury Barbato
Posts:
792
From:
University Federico II of Naples
Registered:
3/15/05


Independent Random Variables
Posted:
Oct 8, 2012 12:38 PM


Hello, I am struggling with the following seemingly very simple probability problem. Let Y, X_1, X_2 three random variables (taking real values) on the same probability space, and suppose that Y and X_1 are independent, as well as Y and X_2. Then, if Y= X_1 + X_2, I think we should have Y = c a.s. for some constant c in R. The proof is trivial if X_1 and X_2 are squareintegrable, because in that case Var(Y)=Cov(Y,X_1 + X_2)=0. But I do not know how to handle the general case. What do you think about? Thank you very very much in advance for your help. My Best Regards, Maurizio Barbato



