Online homework 4, question 4

[Tobias]

Hi there.

I have some understanding how to find g-bar(x). After a lot of tries, I have got to the following solution, but I am far from sure it is valid.
g-bar(x) must be the h(x)=ax, which minimizes the expected squared error for any point, i.e. the expected value of . Since x is uniformly distributed this is the same as minimizing , which yields a=3/pi =0.955

To this I have a few questions

1. Am I correct
2. Does g-bar depend on the size of the sample?
3. Is there a general approach to find g-bar?