Answer:
The expected value of the sample mean is indeed the population mean.
There are two exceptional cases:
(1) if the population mean does not exist (as, for example, with the Cauchy distribution), then the expected value of the sample mean does not exist.
(2) if the population mean is infinite, then the expected value of the sample mean is infinite. (We can blend into this example the negative-infinity case.)
Step-by-step explanation:
The Central Limit Theorem says that the mean of the sampling distribution of the population mean equals the population mean; but it has a standard deviation directly proportional to the population SD, and inversely proportional to the sample size. The mean of all possible means of samples of size N drawn from a population will equal the mean of the population. The variance of that distribution of means will be the variance of the population divided by N.
