Question: An economist has data on the employment status of n individuals. In particular, she has n observations X₁, X₂, ... , X_n, where X_i = 1 if the individual is unemployed and X_i = 0 if the individual is employed. The economist would like to estimate the probability \(\pi \) that an individual is unemployed.

a) Suggest an estimator for \(\pi \). Briefly indicate why yours is a reasonable estimator of \(\pi \).

b) Find the bias, variance, and mean squared error of your estimator.