2. 某種產品之平均不合格率為 0.01，今抽取 n =100 件之樣本，請問其中剛好有 1 件不合格品之機率為何？(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)