MSE estimation and random variables

[rsingh628]

Hello all, I am wondering if my approach is correct for the following problem. My final answer would be c1 = 1, c2 = 0, and c3 = 1. If my approach is incorrect, I certainly appreciate some guidance on the problem. Thank you.

Problem statement:


Approach:

 

[blamocur]

I don't see any errors in your computations.
It is somewhat suspicious that they ask for "optimal" values for c1,c2,c3 but the equations have only one solution.