題組內容

2. Let X1, X2, ..., Xn be a random sample from a population with pdf
\( f(x|\theta) = \theta x^{\theta-1} \mathbf{1}_{\{0<x<1\}}, \theta > 0. \)

(c) \( (5\%) \) Find a consistent estimator of \( \theta \). Prove your claim.