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Let two independent random vectors x and z have Gaussian distributions: p(x) = N(x|µx,Σx), and p(z)...

Let two independent random vectors x and z have Gaussian distributions: p(x) = N(x|µx,Σx), and p(z) = N(z|µz,Σz). Now consider y = x + z. Use the results for Gaussian linear system to find the distribution p(y) for y. Hint. Consider p(x) and p(y|x). Please prove for it rather than directly giving the result.

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