1. 在 40 m2 之地毯中，平均可發現 2 個不合格點，今檢驗 20 m2 之地毯，發現 1 個不合格點之機率為何？(10 分)

4. Let \( X_1, ..., X_n \) be independent RVs having the Negative Exponential distribution with parameter \( \theta \in (0, \infty) \), and set \( U = \sum_{i=1}^n X_i \). Show that the RV \( U \) is distributed as Gamma with parameters \( (n, \theta) \) and that the RV \( 2U/\theta \) is distributed as \( \chi^2_{2n} \). (10 分)