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Let Y = X+N, where X has the exponential distribution with parameter and N is Gaussian with mean 0 and variance 2. The variables X
Let Y = X+N, where X has the exponential distribution with parameter and N is Gaussian with mean 0 and variance 2. The variables X and N are independent, and the parameters and 2 are strictly positive. Find E[X|Y ], the LMMSE estimator and the mean square error for estimating X using E[X|Y ].
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