Problem: In a Gaussian variable experiment, random variables X, Y, Z follow the rule: X,Y\Z are jointly normal with parameters m|z, mylz, Oz|2, Oylz Pr,y|z (all functions of z, in general). (a) What...

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Extracted text: Problem: In a Gaussian variable experiment, random variables X, Y, Z follow the rule: X,Y\Z are jointly normal with parameters m|z, mylz, Oz|2, Oylz Pr,y|z (all functions of z, in general). (a) What is the pdf fælz(r|2)? (b) What is the MMSE of x|y, z? (c) What is the MSE of the MMSE in (b)? (d) Find pr,y, in terms of parameters of z,by using the chain rule (e) Find the MMSE of x z (f) Are x, y, z jointly Gaussian? Explain. (g) When do x, y|z become independent?