# 110 年 - [無官方正解]110 國立高雄大學_碩士班招生考試_經營管理研究所(無組別)：統計學#102198

1.

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.

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.

3. Following 2., Pr( y ≤ 5 )=
(A) (B) (C) (D) 4.4. 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

5.5. 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.

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.

7. n samples are drew from a normal distribution N ( μ , σ2 ) , =
(A)σ2
(B)μ2
(C)σ22
(D) 8.8. 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.

9.9. 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.

10.10. 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.

11. What is the estimated the slope when the regression equation y = α + β x + u passes through the origin?
(A) (B) (C) (D) 12.

12. For positive random variables X and Y , suppose E (Y / X ) = θ X , which of the following is false ?
(A) If a random variable , then E ( Z ) = θ .
(B) The estimator is unbiased for θ .
(C) The estimator is biased for θ .
(D) W2 is not the same as W1 .

13.13. If the residual sum of squares (SSR) in a regression analysis is 60 and the total sum of squares (SST) is equal to 80, what is the coefficient of determination?
(A) 0.25
(B) 0.50
(C) 0.75
(D) 0.90

14.14. Which of the following statement about covariance and correlation coefficient is true?
(A) Correlation coefficient is always less than covariance.
(B) Correlation coefficient and covariance has the same sign.
(C) Correlation coefficient is never equal to covariance.
(D) Correlation coefficient is sensitive to the units of the random variable while covariance is not.

15.

15. 20 white balls and 8 black balls were in a box, then John picks the ball form the box 4 times and does not put the picked ball back into the box each time. If we define random variable X as the number of black ball(s) picked, then Var ( X ) =
(A) (B) (C) (D) 16.16. Which of following distribution is not symmetric to the origin?
(A) uniform distribution with the random variable lying between -2 and 2 .
(B) standard normal distribution
(C) t distribution
(D) X2 distribution

17.

17. X and Y are two random variable, , if E ( X / Y ) = Y 2 , E (Y / X ) = -16 + 2 X , then Cov( X , Y ) =
(A) 1.
(B) 2.
(C) 4
(D) 8.

18.18. Following 17., if Var (Y / X ) = c , then c =
(A) 2.
(B) 4.
(C) 9.
(D) 16.

19.

19. Which of the following probability density functions of a random variable X has E ( X ) = Var ( X ) ?
(A) (B) (C) (D) 20.

20. Two sets of samples { X1 , X2 ,..... X m } and {Y1 , Y2 ,.....Yn } ( m > n ) were drew independently from a population N (μ , σ2 ) , we have two estimator to estimate μ . Which of the following statement is true?
(A) (B) (C) (D) 【非選題】
21.

II.(i) Assume that X has a linear impact on Y in the population as Y = α + βX + ε . We have 22 random samples of ( X , Y ) , and have and R2 = 0.36 .

【題組】

(1) What’s the OLS regression function ? (6%)

【非選題】
22.【題組】

(2) ? Does X have significant impact on Y ? ( α = 0.05 ).(4%) = 0.05 .

【非選題】
23.

(ii) There is a simple regression model with the Gauss-Markov Assumption of Simple Linear Regression (SLR).1 through SLR.5. The OLS estimators and are the unbiased for the respective population parameters α0 and α1  . Let be the parameter obtained from the assumption of a zero intercept.

【題組】

(1) Find in terms of and α1 (3%). Verify that is unbias for α1 when = 0 . (2%)

【非選題】
24.【題組】

(2) Find .(3%) Show that (2%)

【非選題】
25.

III. (i)We have n observations to get OLS regression function .

【題組】

(1) If we regress xi where d 2 ≠ 0 , let be the intercept and be the intercept of the new regress function, please find and ?(6%)

【非選題】
26.【題組】

(2) If we regress on , let be the intercept and be the slope of the new regress function, please find and ? (4%)

【非選題】
27.

(ii) We use n observations to have OLS regression function log y = , where , .

【題組】

(1) If we regress be the intercept and be the slope of the new regress function, please find ?(6%)

【非選題】
28.【題組】

(2) If we regress be the intercept and be the slope of the new regress function, please find ?(4%)

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