In the first scenario, Theta ~N $(0,1)$ and we observe X$=$Theta$+$ W $,$ where W~ N$(0,1)$ is independent of Theta.

In the second scenario, the prior information on Theta is extremely inaccurate: Theta~ N$(0,$ Sigma$0^2),$ where Sigma$0^2$ is so large that it can be treated as infinite. But in this second scenario we obtain two observations of the form Xi$=$Theta $+$ Wi$,$ where the Wi are standard normals, independent of each other and of Theta, MSE is$?$