Is the sample mean always unbiased

E [ μ ^] = e [ ∑ i = 1 n x i n] = μ = e [ x].This follows immediately from the linearity of expectation.It only will be unbiased if the population is symmetric.It is possible to prove that the sample mean is always unbiased.Why is sample mean unbiased estimator?(b) the average sample mean, over all possible samples, equals the population mean.

I'm wondering if the sample mean and sample variance is always an unbiased estimate of the true expected value and variance of the random variable x, where x_i are iid samples.Let us consider the simple arithmetic mean y ¯ = 1 n ∑ i = 1 n y i as an unbiased estimator of population mean y ¯ = 1 n ∑ i = 1 n y i.In other words, is it always true that:The average value of these observations is the sample mean.