I think I have this right but need confirmation.

[medako]

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

 

[tkhunny]

xbar is either unbiased or it isn't. "always" is a strange word. If the expected value of the estimator IS the desired parameter, it's unbiased.

Is it ALWAYS unbiased? Does this mean that one day it will be unbiased and the next it will be biased? Makes no sense.