5. Which of the following statement about a  X²distribution is true?
(A) The shape of its probability density curve depends on the degree of freedom.
(B) It is a symmetric distribution.
(C) The value of the random variable can be negative.
(D)It is a ratio of two t distributions.

8. If random variable X is uniformly distributed between 2 and 4 , then Var (X) = (A) (B)(C)  (D)

9. In a simple OLS regression function, which of the following distribution can be used to test whether X has a significant impact on Y ? (A) binomial distribution (B) t distribution (C) chi-square distribution (D)hypergeometric distribution

10. The distribution of a standardized random variable will approach a standard normal distribution when the sample size is large enough is called________ . (A) The central limit theorem (B) Law of big data (C) Law of normal distribution. (D)Law of large number

11. To test that per capita GDP of Taiwan in 2019 is no less than twenty thousand US dollars, if the significant level is 5%, which of the following statement is true? (A) Two tailors test is needed. (B) Right tailor is needed. (C) If the P-value is 0.03, then we cannot rejected null hypothesis. (D)For a given sample, the P-value is negatively related to the per capita GDP level that we want to test.

12. If random variables X and Y are independent, and V(X ) = 20 ,V ( Y) 16 = ，then V(2X+ 0.5Y ) = (A) 48. (B) 64. (C) 84. (D)96.

13. The sum of three binomial random variables is a (A) Poisson distribution. (B) Laplace distribution. (C) hypergeometric distribution. (D)normal distribution.

14. Which of the following statements about the property of an estimator is not true ? (A) Unbias cannot assure consistent. (B) Consistent not necessarily assures unbias. (C) There are only one estimator with the properties of both unbias and consistency. (D)An unbias estimator is not necessarily more efficient than a bias estimator.

15. When we use n random samples to obtain the OLS regression function the coefficient of determination 2 R is not equal to (A) (B) (C) (D)

16. In general, we use_________ to test whether the variance of two populations are equal. (A) z-test (B) t-test (C) X2  test (D) F test

17. According to Chebyshev inequality, the probability that the distance between a random variable and the expected value of the random variable is no greater than three times of standard deviation is no less than (A) (B) (C) (D)

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