題組內容

1. (50%) Let $X1, X2, \ldots, X_n$ be a random sample of size n from a distribution that has pdf

$$f(x) = \frac{1}{\theta} \exp \left[ - \left( \frac{x - \alpha}{\theta} \right) \right], \alpha \le x < \infty.$$



(a) (5%) What is the mean of \( X_{i} \)? Justify your answer.