MSE estimation with random variables

[ashah99]

Homework Statement

Please see attached problem

Relevant Equations

MSE = E( (Xhat[k] - X[k])^2 )

Hello all, I would appreciate any guidance to the following problem. I have started on parts (a) and (b), but need some help solving for the coefficients. Would I simply take the expressions involving the coefficients, take the derivative and set it equal to 0 and solve? I believe I also need the variance (for part (c) for instance) $Var(U_K)$ but using the formula (b-a)^2/12 (which would be (3-(-3)^2/12 = 3) from the uniform distribution seems wrong. Any help appreciated

Problem:

Approach so far:

 

[lippyka]

(a) $$U_K = \alpha + \beta x_1 + \gamma x_2 + \delta x_3$$(b) $$\frac{1}{n}\sum_{i=1}^{n}(U_K - \hat{U_K})^2 = \frac{1}{n}\sum_{i=1}^{n}(\alpha + \beta x_{1i} + \gamma x_{2i} + \delta x_{3i} - \hat{U_K})^2$$(c)Var(U_K) = ?