題組內容

4、Let f(x; θ) = (1/θ)x⁽¹⁻⁰⁾/θ, 0 < x < 1, 0 < θ < ∞. Let X₁, X₂, ..., Xₙ denote a random sample of size n from this distribution.

(2) \( (5\%) \) Show \( \operatorname{E}(\hat{\theta}) = \theta \) and thus \( \hat{\theta} \) is an unbiased estimator of \( \theta \).