週三"阿摩用功日",VIP 免費領取 前往領取
馨小妞>試卷(2021/10/15)

研究所、轉學考(插大)◆統計學題庫 下載題庫

無法測驗完立即知道正確答案,需要等候一段時間。

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 

選擇:20題,非選:8題
立即測驗 
我要補題 回報試卷錯誤
1.

1. x1 , x2 , x3 ,...., xn are randomly samples from a normal population N ( μ , σ2 ) . If we use  61692386b4829.jpg to estimate σ2 , then 6169239cb9b65.jpg =
(A) 616923acb02ca.jpg
(B)σ2 
(C) 616923c14b738.jpg
(D) 616923c6bfebb.jpg



2.

2. A continuous random variable X has the following probability density function: f ( x) = 616923ee55c00.jpg , 0 ≤ x ≤ 2 . If we have another other random variable Y = 3 X2 + 2 , the probability density function of Y is
(A) 6169243b42882.jpg
(B) 6169244206c47.jpg
(C)f(y)=3(4y-1)2+2
(D) 616924483ba14.jpg



3.

3. Following 2., Pr( y ≤ 5 )=
(A) 6169246c14413.jpg
(B) 616924721d56f.jpg
(C) 61692479251b7.jpg
(D) 6169247eaeaa6.jpg



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 : 616924ad06b54.jpg 616924b6461cd.jpg , the which of the followings is not true ?
(A) p lim x = 1 .
(B) 616924c97ba27.jpg
(C) 616924d8c0c2a.jpg
(D) x will converge to a given vale.



7.

7. n samples 616924ed38769.jpgare drew from a normal distribution N ( μ , σ2 ) , 6169250b5c6fd.jpg=
(A)σ2 
(B)μ2
(C)σ22 
(D) 6169253eeebc6.jpg



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) 616925913c5be.jpg
(B) 616925992390e.jpg
(C) 6169259eba0c7.jpg
(D) 616925a39d3a0.jpg



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 616925be6e0f6.jpg , then E ( Z ) = θ .
(B) The estimator 616925ed1d2e3.jpg is unbiased for θ .
(C) The estimator 616926088077c.jpg 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) 6169263982713.jpg
(B) 6169263f9a612.jpg
(C) 6169264570b5f.jpg
(D) 6169264a5c12d.jpg



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, 616926786bd40.jpg , 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) 616926bad400e.jpg
(B) 616926c707794.jpg
(C) 616926ce0000b.jpg
(D) 616926d380a2d.jpg



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 6169270da16eb.jpg to estimate μ . Which of the following statement is true?
(A) 61692735de014.jpg
(B) 6169273d74c66.jpg
(C) 6169274a44e80.jpg
(D) 616927518f4ee.jpg



【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 616927916b879.jpg and R2 = 0.36 .


【題組】

(1) What’s the OLS regression function 616927b08f68b.jpg? (6%)



【非選題】
22.【題組】

(2) 616927c0e5d7b.jpg? Does X have significant impact on Y ? ( α = 0.05 ).(4%)
               616927ec6cd6a.jpg = 0.05 .



【非選題】
23.

(ii) There is a simple regression model 61692813341f4.jpg with the Gauss-Markov Assumption of Simple Linear Regression (SLR).1 through SLR.5. The OLS estimators 61692831e3d7b.jpg and 616928388ba75.jpg are the unbiased for the respective population parameters α0 and α1  . Let 61692877f19c7.jpgbe the parameter obtained from the assumption of a zero intercept.


【題組】

(1) Find 616928b00358d.jpgin terms of 616928b9cec79.jpg and α1 (3%). Verify that 616928db730e6.jpg is unbias for α1 when 616928edb135b.jpg = 0 . (2%)



【非選題】
24.【題組】

(2) Find 6169290b9e5f3.jpg .(3%) Show that 616929136f2e8.jpg (2%)



【非選題】
25.

III. (i)We have n observations to get OLS regression function 6169292927fe2.jpg .


【題組】

(1) If we regress 61692945cb834.jpg xi where d 2 ≠ 0 , let 61692964f393c.jpg be the intercept and 616929707406d.jpg be the intercept of the new regress function, please find 61692979d8047.jpg and 6169298010fbf.jpg ?(6%)



【非選題】
26.【題組】

(2) If we regress 6169299fb0acc.jpgon 616929a6705d6.jpg, let 616929b653bcb.jpg be the intercept and 616929bced916.jpg be the slope of the new regress function, please find 616929c3f2bce.jpg and 616929cda61ed.jpg? (4%)



【非選題】
27.

(ii) We use n observations to have OLS regression function log y = 61692af616869.jpg , where 61692b01eba00.jpg , 61692b1274f1e.jpg .


【題組】

(1) If we regress 61692b4345d5b.jpg be the intercept and 61692b4c76027.jpg be the slope of the new regress function, please find 61692b52b7846.jpg ?(6%)



【非選題】
28.【題組】

(2) If we regress 61692b7b9d131.jpg be the intercept and 61692b82b5360.jpg be the slope of the new regress function, please find 61692b8a61aa5.jpg?(4%)



懸賞詳解

國二社會上第三次

33.有關「靖難之變」與「三藩之亂」的比較敘述,下列何者正確? (甲)皆是因皇帝進行削藩而引起 (乙)前者屬於宗室叛變 ;後者屬於地方諸侯叛變。 ...

50 x

前往解題

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-阿摩線上測驗

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