$MSE(θ_1) = MSE(θ_2) = 0.06$?

Question

We offer two estimators for the average concentration $μ$ of lead in the atmosphere of a region of Quebec where factories manufacturing dyes are located. The first estimator $θ_1$ has a bias equal to 0.2 and a variance of 0.02. The second estimator $θ_2$ is unbiased and has a variance equal to 0.06.

Which of the following is true?

1. $θ_1$ is better than $θ_2$ to estimate $μ$.
2. $θ_2$ is better than $θ_1$ to estimate $μ$.
3. None of the above is true

I have some difficulties to find the right one. If I use the mean square error (MSE), then $MSE(θ_1) = MSE(θ_2) = 0.06$. So does the the choice 3 is the right one?

Answer 1

The two estimators have the same MSE but $\theta_2$ is correct while $\theta_1$ is biased

For a moment forget all you studied and answer intuitively: which one do you prefer?