A obtain a umvue of and calculate its variance b obtain a

Question

Let (X₁, Y₁), ...,(X_n, Y_n) be i.i.d. random 2-vectors distributed as bivariate normal with EX_i = EY_i = βz_i, Var(X_i) = Var(Y_i) = σ², and Cov(X_i, Y_i) = ρσ², i = 1, ..., n, where β ∈ R, σ > 0, and ρ ∈ (-1, 1) are unknown parameters, and z_i's are known constants.

(a) Obtain a UMVUE of β and calculate its variance.

(b) Obtain a UMVUE of σ² and calculate its variance.