Doubling the Mean Versus the Maximum
A sample of n = 10 independent observations is drawn from the uniform distribution on [0, θ]. Consider two unbiased estimators of θ: A = 2X̄ (twice the sample mean) and B = ((n + 1)/n) · max(X₁, ..., Xₙ). What is the ratio Var(A)/Var(B)?
Related problems
Source: Classic comparison of estimators for the endpoint of a uniform distribution; textbook material. Statement written for AxiomIQ.