Mathematics · Linear Models & Regression

Consider the linear model: Y1 = β1 + β2 + ε1 Y2 = β1 + 2β2 + ε2 Y3 = β1 + cβ2 + ε3 where β1, β2 ∈ &mathbb;R are unknown parameters, and uncorrelated errors εi have zero mean and variance σ2 > 0. The constant c is such that β̂1 and β̂2 are uncorrelated, where β̂1 and β̂2 are the best linear unbiased estimators of β1 and β2. What is (Var(β̂1), Var(β̂2))?