題組內容

1. (15%) Let $f(x; \theta) = (1/\theta)x^{(1-\theta)/\theta}$, $0 < x < 1$, $0 < \theta < \infty$.

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