Consider a population with mean 𝜇 and variance 𝜎 2 < ∞ . You are comparing two estimators 𝜇 ̂ 1 and 𝜇 ̂ 2 for the mean of the population 𝜇 , with the following expected values and variances 𝐸 ( 𝜇 ̂ 1 ) = 𝜇 ; 𝑉 ( 𝜇 ̂ 1 ) = 9 ; 𝐸 ( 𝜇 ̂ 1 ) = 𝜇 + 1 ; 𝑉 ( 𝜇 ̂ 2 ) = 1 . We also know that the covariance between the two estimators is 𝐶 𝑂 𝑉 ( 𝜇 ̂ 1 , 𝜇 ̂ 2 ) = − 2 . Now consider a new estimator that combines the two previous ones 𝜇 ̂ 3 = 1 4 𝜇 ̂ 1 + 3 4 𝜇 ̂ 2 . Then the variance 𝑉 ( 𝜇 ̂ 3 ) of 𝜇 ̂ 3 is