1. Which of the following properties are important for any estimator to possess?

A. Bias

B. Inconsistency

C. Consistency

D. Achieves the Cramer-Rao Lower Bound

E. Efficiency

a. C and D

b. A, B, and E

c. A, B, and C

d. None of the above.

e. C, D, and E

2. Consider the sample mean estimator. Moreover, we are drawing a random sample of size 100 from the normal population. Which of the following is incorrect?

A. The sample mean estimator is also the maximum likelihood estimator but not the method of moments estimator.

B. The sample mean estimator is also the method of moments estimator but not the maximum likelihood estimator .

C. The sample mean estimator has a mean that is not similar to the mean of the normal distribution from which the random samples are drawn.

D. The variance of the sample mean estimator is always equal to the variance of the normal distribution.

E. The variance of the sample mean estimator is always equal to the variance of the normal distribution divided by the size of the sample mean estimator.

a. A and E

b. All of the above.

c. B and D

d. C, D, and E

e. None of the above.

f. A and B

3. An estimator is consistent if it converges to the true parameter asymptotically. If the estimator is consistent, its density will maintain its shape no matter how large the sample size is.

a. True

b. False