112年 - 112 國立臺北大學_碩士班一般入學考試試題_企業管理學系甲組：統計學#146873

1. (10%) Given below is a bivariate distribution for the random variables a and b. Find the correlation coefficient of a and b.

(Note: You are being asked to calculate to two decimal places)

2. (20%) Given below is a machine with five components and the reliability probability of each component is 0.9. Find the reliability probability of this machine.

(Note: You are being asked to calculate to four decimal places)

3. (20%) If random variable X is normally distributed with mean μx and variance σ²x. Find the expectation of |X - μx|.

(1) \( \varepsilon_{i} \) 分布不為常態；(5%)

(2) \( \varepsilon_{i} \) 期望值不為0；(5%)

(3) \( \varepsilon_i \) 變異數不同質 (即 \( \text{Var}(\varepsilon_i) \neq \sigma^2 \))；(5%)

(4) 誤差項間共變(即 \( \operatorname{Cov}(\varepsilon{i}, \varepsilon{i}) \neq 0, i \neq j \))；(5%)

(5) \( X{1} \) 與 \( X{2} \) 有明顯的共線性。(10%)

(1) 這個<顯著交互效果>的意義是什麼？(10%)；

(2) 後續應該進行什麼檢定？(10%)