设 X_1, X_2, ..., X_n 为取自总体 X 的一个样本，总体 X 的密度函数为[ f(x; theta_1, theta_2) = (1)/(theta_2) e^-(x-theta_1)/(theta_2), -infty < theta_1 < x < infty, theta_2 > 0 ](1) 求 theta_1, theta_2 的矩估计量；(2) 求 theta_1, theta_2 的极大似然估计量.

(1) 矩估计量：$\hat{\theta}_1 = \bar{X} - S$，$\hat{\theta}_2 = S$，其中 $S = \sqrt{\frac{1}{n} \sum_{i=1}^n (X_i - \bar{X})^2}$。 (2) 极大似然估计量：$\hat{\theta}_1 = \min(X_1, X_2, \ldots, X_n)$，$\hat{\theta}_2 = \frac{1}{n} \sum_{i=1}^n (X_i - \hat{\theta}_1)$。 \[ \boxed{ \begin{array}{cc} \text{(1) 矩估计量：} & \hat{\theta}_1 = \bar{X} - S, & \hat{\theta}_2 = S \\ \text{(2) 极大似然估计量：} & \hat{\theta}_1 = \min(X_i), & \hat{\theta}_2 = \frac{1}{n} \sum_{i=1}^n (X_i - \hat{\theta}_1) \end{array} } \]