Which of the following statements are true if is a random sample from a distribution with mean mu?

A. The sample mean xbar is always an unbiased estimator of the population mean mu .

B. The sample median,
, is an unbiased estimator of the population mean, mu ,if the distribution is continuous and symmetric.

C. Any trimmed mean is an unbiased estimator of the population mean,mu ,if the distribution is continuous and symmetric.

D. None of the above

E. All of the above

I believe the answer is D but am feeling unsure. I had A then I noticed it said ALWAYS and that is not true

A. The sample mean xbar is always an unbiased estimator of the population mean mu .

B. The sample median,

C. Any trimmed mean is an unbiased estimator of the population mean,mu ,if the distribution is continuous and symmetric.

D. None of the above

E. All of the above

I believe the answer is D but am feeling unsure. I had A then I noticed it said ALWAYS and that is not true

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