五、人體基因序列解碼計畫 (Human Genome Project)：2001 年已經完成人體基因 DNA 序列的解碼工作，並可由這些序列得到許多有用的資訊，請問對藥物開發影響為何？(15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)