1. x₁ , x₂ , x₃ ,...., xn are randomly samples from a normal population N ( μ , σ² ) . If we use  to estimate σ² , then =
(A)
(B)σ² 
(C)
(D)

2. A continuous random variable X has the following probability density function: f ( x) = , 0 ≤ x ≤ 2 . If we have another other random variable Y = 3 X2 + 2 , the probability density function of Y is (A) (B) (C)f(y)=3(4y-1)2+2 (D)

3. Following 2., Pr( y ≤ 5 )= (A) (B) (C) (D)

4. When the distribution of a random variable is symmetric, which of the following parameters is zero? (A) mean (B) variance (C) third moment (D) fourth moment

5. Which of the following statements is true? (A) In a simple regression model, the determinant is zero means there is no relation between the dependent and independent variables. (B) If the distribution of the disturbance term is not a normal distribution, then the OLS estimator cannot be unbias. (C) If the intercept of the regression function is very close to zero, we can infer that the intercept is not significantly different from zero. (D) If we use t-distribution to test whether the coefficient of the regression function is significantly differently from zero, the distribution of the OLS estimator of the coefficient should be a normal distribution.

6. The probability density function of discrete random variable x is : , the which of the followings is not true ? (A) p lim x = 1 . (B) (C) (D) x will converge to a given vale.

7. n samples are drew from a normal distribution N ( μ , σ2 ) , = (A)σ2 (B)μ2(C)σ2+μ2 (D)

8. X , Y , Z are random variables, which of the following statement about conditional means is not true? (A) E[ E (Y / X )] = E (Y ) . (B) If X and Y are independent, then E (Y / X ) = E (Y ) . (C) E (Y / X ) = E[ E (Y / X , Z ) / X ] . (D) If Cov( X , Y ) = 0 , then E (Y / X ) = E (Y ) must hold.

9. Which of the following results of sampling rejects the null hypothesis that the population mean is significantly different from than 0. (A) p-value is very low. (B) t-value is positive. (C) The confidence interval of the sample mean includes 0. (D) t-value is negative and close to zero.

複選題10. Which of the following statement is true? (A) In hypothesis testing, if we fail in rejecting the null hypothesis when it is actually false, then we make a Type I error. (B) When we have the same sample to test the mean of a population around a specific value, it is more likely to reject the null hypothesis when we use one-tailed test than when we use two-tailed test under the same significant level. (C) The probability of t-value less than that of the critical t-value of a significance level is equal to p-value. (D) Using confidence interval to see whether it includes the specific population parameter may make different inference from doing hypothesis testing.

11. What is the estimated the slope when the regression equation y = α + β x + u passes through the origin? (A) (B) (C) (D)

113年 - 113 國立臺灣大學_碩士班招生考試：工程統計#119664

112年 - 112 國立臺灣大學_碩士班招生考試試題：工程統計#119662

111年 - 111 國立臺灣科技大學_碩士班招生試題：統計學(C)#120895

110年 - 110 國立陽明交通大學_碩士班考試入學試題：統計學#121574

110年 - 110 國立臺灣科技大學_碩士班招生試題_企業管理系：統計學#111322

110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:統計學(H)#111297

110年 - 110 國立政治大學_碩士班暨碩士在職專班招生考試_財政所:統計學#110890

110年 - 110 國立高雄科技大學_碩士班招生考試_工業工程與管理系：統計學#110420

110年 - 110 國立政治大學_碩士班招生考試_財政研究所:統計學#107983

110年 - 110 國立政治大學_碩士班招生考試_ 國際經營與貿易學系:統計學#106074