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.

(b) \( (5\%) \) Let \( Y{2} \) denote the second smallest item from this sample. Find the limiting distribution of \( W{n} = nF(Y_{2}) \).