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The random vector (X, Y) has a two-dimensional normal distribution with Var(X) =Var(Y). Show that X+Y and XY are independent random variables. PLEASE do not

The random vector (X, Y) has a two-dimensional normal distribution with Var(X) =Var(Y). Show that X+Y and XY are independent random variables.

PLEASE do not copy the exact answer from Chegg. I am trying to study for my exam coming up.

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