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交大◆電機◆線性代數與機率

交大◆電機◆微分方程與線性代數

交大◆電機◆線性代數與機率

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6. Consider the linear population model with intercept:$y_t = \alpha + \beta x_t + \varepsilon_t$The variance structure is known as below: $E(\varepsilon_t^2) = \sigma^2 h_t^2,$Which regression may obtain efficiency $\hat{\beta}$ estimator? (A) Regress \( y_{t} \) on 1, \( x_{t} \) (B) Regress \( y_{t} / h_{t} \) on 1/ht ,xt/ht(C) Regress \( y_{t} / h_{t}^{2} \) on 1/h2t ,xt/h2t(D) Regress \( y_{t} \) on 1/ht ,xt/ht(E) Regress \( y_{t} / h_{t} \) on 1, \( x_{t} \)

5. Consider the linear model with intercept: $y_t = \alpha + \beta x_t + u_t$ If the $A = \sum_{i=1}^{n} (x_i - \bar{x})^2$ is positive definite and $E(u_i \mid x_i) = 0, \forall t = 1, 2, \dots, T$, which statement is true under sample size $T \to \infty$. (A) \( \hat{\beta} \) is consistent, but we cannot judge whether \( \hat{\beta} \) is efficiency (B) \( \hat{\beta} \) is unbiased and efficiency (C) \( \hat{\beta} \) is consistent and efficiency (D) \( \hat{\beta} \) is, but we cannot judge whether \( \hat{\beta} \) is efficiency (E) \( \hat{\beta} \) is unbiased and consistent.

4. Consider the simple regression $y_i = \alpha + \beta x_i + \varepsilon_i$And suppose population parameter $\beta = 2$ and least square estimator $\hat{\beta} = 2.3$. Now consider the regression $(x_i - y_i) = \alpha^* + \beta^* x_i + u_i.$What is the value of \( \hat{\beta} \)? (A) 1 (B)-1 (C)-1.3 (D)-0.3 (E) 0.3

五、請說明國道電子收費與外部性的關係，並分析尖峰和非尖峰時段是否應收取相同費率。(15 分)

四、政府實行所得重分配政策是否可以提高經濟效率？為什麼？(20 分)

三、社會安全退休年金制度對個人儲蓄行為有哪些可能的影響？(15 分)

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43. 李先生 75 歲，因呼吸急促到急診，胸部 X 光顯示左側肋膜有積液，下列肋膜液分析結果 何者不屬於滲出液 ( exudate ) 的特性？ (A)Pleural fluid pH < 7.30 (B)Pleural fluid : serum protein ratio < 0.5 (C)Pleural fluid : serum LDH ratio > 0.6 (D)Pleural fluid LDH > 0.67 upper limit of normal for serum LDH

73.下列胸水檢查結果何者較不像是 exudate？ (A) pleural fluid protein level ＞ 3.0 g/dL(B) pleural fluid: serum protein ratio ＞ 0.5(C) pleural fluid lactic dehydrogenase ＜ 100 IU/L(D) pH 值 ＜ 7.20

1 “As a result, climate change is likely to deepen existing global inequalities.” Millions of people in East Africa are suffering from severe drought, while violent storms continue to damage parts of Southeast Asia. Coffee farmers in Central America are also facing declining yields due to rising temperatures. (A) Poorer nations are generally less able to cope with such environmental changes and are often located in regions where climate conditions are more extreme. (B) As global temperatures rise, these countries are expected to bear the greatest burden. (C) Experts estimate that by 2030, billions of dollars will be required annually for adaptation efforts. (D) In addition, higher borrowing costs make it even more difficult for these nations to respond effectively. (E) This may lead to a worsening cycle of vulnerability and financial strain

2. "Meanwhile, it has also diverted attention from other ongoing global threats." The COVID-19 pandemic has shown how a global risk can quickly become a widespread crisis, affecting both public health and economic stability. (A) In the short term, it has intensified problems such as job losses and declining social trust. (B) At the same time, long-term challenges like climate change and technological inequality remain unresolved. (C) Although vaccines were developed rapidly, the crisis revealed the limits of reactive responses. (D) Greater preparation and international cooperation might have reduced the damage. (E) This experience highlights both the risks the world faces and the opportunity to build a more resilient future.

18 關於刑法公共危險罪章之適用，下列敘述何者錯誤？ (A)甲將汽油潑灑至某一現供人使用之住宅後，點燃手中的噴槍，依實務見解，尚不屬於刑法第 173 條放火罪之著手(B)乙對某一現有人所在之建築物放火，僅燒燬屋內家具，而房屋主結構並未受損，依實務見解，尚不構成刑法第 173 條第 1 項之放火罪(C)丙為報復，向緊鄰加油站之加油機的無人小客車投擲汽油彈，致車輛全毀，構成刑法第 175 條第 1項之罪(D)丁為詐領保險金，明知久未供使用之空屋附近有遊民居住，仍放火燒燬自己所有之該屋，構成刑法第 174 條第 2 項之罪

144. 以一含內阻之電源提供負載功率，當負載獲得最大輸出功率時，其傳輸效率為何？ 鐵路、國安特考 112 (A)25% (B)50% (C)60% (D)80%