題組內容

3. Let $X_1, X_2, \ldots$, and $X_n$ be a random sample from distributions with the following probability density functions. In each case find the maximum likelihood estimator $\hat{\theta}$.

(a) \( (5\%) f(x; \theta) = \theta x^{\theta - 1}, 0 < x < 1, 0 < \theta < \infty \)