3. 若 Z N~ (0,1) 具有機率密度函數為 fz() 及累積分配函數為 Fz() ，試求 EFZ [ ()]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)