True or False (If the statement is false, please explain.) 1. Statistics are bas

Question

True or False (If the statement is false, please explain.)

1. Statistics are based on random sample and values are unknown.

2. For 2 or more random variables, we can always derive the joint pdf from marginal pdf's

3. Estimators that are unbiased and have minimum variance are the best estimators

4. Sample SD is unbiased estimator for population SD

5. Central limit theorem states that the sample means distribute as normal, if and only if the distribution of the population is normal

6. maximum likelihood estimators are always unbiased estimators

7. If the joint pdf between X and Y are bivariate normal, then the marginal of X and marginal of Y are always normal

8. If the marginal of X and Y are both normal, then the joint between X and Y are always bivariate normal

9. If X is normal, and Y is normal, then X+Y is also normal

10. The marginal pmf of multinomial is always a binomial

11. The sample mean is distributed as normal, if and only if the distribution of the population is continuous

12. The correlation is bounded by 0 and 1

13. The correlation is bounded, while the covariance has no boundary for its value

14. If the correlation between X and Y is 0, then they are independent

15. MSE of an estimator is the sum of bias and variance of the estimator

16. If a 95% CI of the population mean is (11,12), then there is a probability of 95% that the true population mean is between 11 and 12

17. Based on the same sample, a 95% CI is wider than the 99% CI

18. CI gets wider, as n gets larger.

19. CI for SD is simply the square root of CI for variance

20. Based on a sample of binomial data, a 95% CI for p could contain negative value, for example, (-0.1, 0.3).

Explanation / Answer

1. True. It's trivial. Statistics is study of quantifying uncertainty. so values will have to be unknown.
2.No. The conditional distribution is necessary to be know.

3.True.we always look for minimising variance.

4.True. sample sd with denominator n-1. it can be proved rigorously taking expection on sample sd. it's a popular result.

here we solve only 1st four parts of a question.

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