Help with linear and unconstrained MMSE estimators

#1
Hello all, would anyone be willing to provide assistance on calculating the linear and unconstrained MMSE estimators for Gaussian random variables?
The problem statement I have is shown below. Any insights are much appreciated!
 

Attachments

hlsmith

Less is more. Stay pure. Stay poor.
#2
a) looks like it is just requesting you model a least squares (simple linear regression).

As for b.), I am not familiar enough to know what they are looking for, polynomials?