Question: please provide detail process 5. (10 points) Suppose that X and Y are independent standard normal distributions. Show that U = (X +Y) and V

please provide detail process

5. (10 points) Suppose that X and Y are independent standard normal distributions. Show that U = (X +Y) and V = (X - Y) are also independent standard normal distributions. You may assume that (U, V ) is a bivariate normal. Hint: Find the mean and variance of U and V, as well as p = Corr(U, V).]

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