題組內容

3. (50%) Let $X1, X2, \dots, X_n$ be a random sample of size $n$ from a distribution that has pdf

$$f(x) = \theta(1 - x)^{\theta-1}, \quad 0 < x < 1, \theta > 0.$$



(a) \( (10\%) \) Find the maximum likelihood estimator of \( 1 / \theta \)