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

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

(b)(10%) DERIVE the cumulative distribution function of \( Y_n \), which is defined as the minimum of \( X_1, X_2, ..., X_n \). (Do not use the formula for the CDF of order statistics.)