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Problem 1. Suppose X and Y are independent standard normal random variables. (a) Write down the joint density of X and Y. (b) The answer to part (a) is an example of a bivariate normal density, which is in general given by the following expression: fwew[eeeeww a) 27rorxoy 1p2 '3an What values of the ve parameters 0X, (Ty, pr, m, and pin the above expression yield the joint density in part (a)