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

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

(c) (10%) Does \( Y_{n} \) converge in probability? If yes, what random variable does it converge to? Prove the convergence or divergence.