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.

(d) \( (5\%) \) Find the maximum likelihood estimator (MLE) \( \theta_{n} \) of \( \theta \)