題組內容

2. (30%) Let X₁, X₂, ..., Xₙ be a random sample drawn from the pdf

$$f(x) = e^{(-(x-\theta))}, x > \theta; -\infty < \theta < \infty$$

and F(x) denotes the corresponding distribution function.



(a) \( (5\%) \) Let \( Y{1} = \min \{X{1},\dots,X{n}\} \). Show that \( Y{n} \) is a consistent estimator of \( \theta \).