Question: We are interested in measuring a certain quantity modeled by a random variable x ~ with zero mean and unit variance. Our available measurements y

We are interested in measuring a certain quantity modeled by a random variablex~ with zero mean and unit variance. Our available measurementsy~=x~+z~ are corrupted by additive random noise, modeled as a random variablez~ with zero mean and variance ² , which is independent from x~.

(a) What is the best linear estimate of x~ given y~=y?

(b) What is the corresponding mean squared error?

(d) What happens to the estimate and the error when ? Explain why this makes sense.

Ref: Probability and Statistics

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