I am stuck at the following exercise: Let $ (X_k)_k$ be a sequence of i.i.d. Bernoulli$ (p)$ distributed RVs with $ p=1/2$ . We want to estimate $ Var(X_1) = p(1-p) = p^2 =: \tau_p^2$ by directly plugging in the natural estimator $ \widetilde{p} := \frac{1}{n}\sum_{i=1}^n X_i$ of $ p$ . We call this estimatorRead more