Solution
= Solution
Independence gives $\mathbb E\|Y^*-HY\|^2=\|(I-H)μ\|^2+nσ^2+σ^2\operatorname{tr}H^2$. Comparing with part (b) shows the difference is $2σ^2\operatorname{tr}H$, proving unbiasedness.
= Solution
Independence gives $\mathbb E\|Y^*-HY\|^2=\|(I-H)μ\|^2+nσ^2+σ^2\operatorname{tr}H^2$. Comparing with part (b) shows the difference is $2σ^2\operatorname{tr}H$, proving unbiasedness.