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Consider the following probability distribution. Complete parts a through f below. x D 1 1 1 p(x) *** 27 9 2/ 9 9 27 (Type integers or simplified fractions.) c. Find the sampling distribution of the median, M, of a sample of n = 3 observations from this population. Type the answers in ascending order for M. M 1 4 7 7 13 7 p(M) 27 27 27 (Type integers or simplified fractions.) d. Refer to parts b and c, and show that both the mean and median are unbiased estimators of μ for this population. E(x) = 4, E(M)= 4, and from part a, µ = 4. Therefore, E(X) = μ and E(M) = μ. This shows that the mean and the median are unbiased estimators of μ for this population. (Type integers or decimals rounded to two decimal places as needed.) e. Find the variances of the sampling distributions of the sample mean and the sample median. 24-0 (Type integers or decimals rounded to two decimal places as needed.)
1. Which estimator would you use to estimate p? Why? OA. Since both the sample mean and median are unbiased estimators, use the sample median, M, because it has the larger variance. OB. Since both the sample mean and median are unbiased estimators, use the sample mean, x, because it has the smaller variance. OC. Since both the sample mean and median are unbiased estimators, use the sample median, M, because it has the smaller variance. OD. Since both the sample mean and median are unbiased estimators, use the sample mean, x, because it has the larger varience