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Let X ~ N (1, 2^2) and Y ~ N (2, 2^2). Suppose that X and...

Let X ~ N (1, 2^2) and Y ~ N (2, 2^2). Suppose that X and Y are independent. Let U = X + Y and V = X ̶Y. Show that U and V are independent normal random variables. Find the distribution of each of them.

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Here we use additive property of normal distribution.

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