Observations Y1,... ,Yn are made according to the model Yi = + xi + i, where x1,...,xn are fixed constants and 1,...,n are iid

Observations Y1,... ,Yn are made according to the model Yi = α + βxi + εi, where x1,...,xn are fixed constants and ε1,...,εn are iid n(0, σ2). Let  and  denote MLEs of α and β.
(a) Assume that x1,...,xn are observed values of iid random variables X1,...,Xn with distribution n(μX, σ2X). Prove that when we take expectations over the joint distribution of X and Y, we still get E = α and E = = β.
(b) The phenomenon of part (a) does not carry over to the covariance. Calculate the unconditional covariance of  and  (using the joint distribution of X and Y).