Question: Let X ~ n(, 2) and let Y ~ n(, 2). Suppose X and Y are independent. Define U = X + Y and V

Let X ~ n(μ, σ2) and let Y ~ n(γ, σ2). Suppose X and Y are independent. Define U = X + Y and V = X - Y. Show that U and V are independent normal random variables. Find the of each of them.

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