2. (20%) The density function for the triangular distribution is given byf(y) = y + 1 - x for x - 1 < y ≤ x andf(y) = -y + 1 + x for x < y ≤ x + 1Find the mean absolute deviation $E[|Y - x|]$.

4. (10%) 某研究生建立迴歸模式：$ Y_i = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \beta_3 X_{3i} + \varepsilon_i $，$ \varepsilon_i $ 是誤差，$ i = 1, 2, 3, ..., n $，$ \varepsilon_i $ 滿足基本假設。估計結果顯示 $ \beta_1 $ 的估計值(b1)在 95% 信賴水準下達顯著($ H_1: \beta_1 > 0 $, t-value = 2.06)，但 $ X_1 $ 的 VIF (variance inflation factor) 值為 9。請問：如果 VIF 值為 4，那 $ \beta_1 $ 的估計值 95% 信賴水準下是否會轉為不顯著？為什麼？

2. (20%) The density function for the triangular distribution is given by

$$f(y) = y + 1 - x \quad \text{for} \quad x - 1 < y \leq x \quad \text{and}$$

$$f(y) = -y + 1 + x \quad \text{for} \quad x < y \leq x + 1$$

Find the mean absolute deviation $E[|Y - x|]$.

相關申論題

相關試卷

2. (20%) The density function for the triangular distribution is given by$$f(y) = y + 1 - x \quad \text{for} \quad x - 1 < y \leq x \quad \text{and}$$$$f(y) = -y + 1 + x \quad \text{for} \quad x < y \leq x + 1$$Find the mean absolute deviation $E[|Y - x|]$.

相關申論題

相關試卷

2. (20%) The density function for the triangular distribution is given by

$$f(y) = y + 1 - x \quad \text{for} \quad x - 1 < y \leq x \quad \text{and}$$

$$f(y) = -y + 1 + x \quad \text{for} \quad x < y \leq x + 1$$

Find the mean absolute deviation $E[|Y - x|]$.