2. (35%) Let \( X_i, i = 1, ..., n \), be an exponential random sample with the probability density function \[ f(x; \lambda) = \lambda \exp(-\lambda x), x \geq 0; \lambda > 0. \] Let the distribution function of \( f(x; \lambda) \) be denoted as \( F(x; \lambda) \). Also, let \( X_{(i)}, i = 1, 2, ..., n \), denote the order statistics of \( X_i, i = 1, 2, ..., n \), where \( X_{(1)} \leq X_{(2)} \leq \cdots \leq X_{(n)} \). The detailed derivation has to be provided for all the following problem. No point is given when only answers are given.