proof of the sample mean being the unbiased estimator of population mean in Simple Random Sampling with Replacement

Question

Im'm looking for the simplest proof of the sample mean being the unbiased estimator of population mean in Simple Random Sampling with Replacement.

I searched for this in literature in my native language but I couldn't find anything satisfactory. Thanks for help!

Answer 1

With appropriate definitions, and bits of explanation:

$E(\bar X) = \frac{1}{n}\sum_{i=1}^n E(X_i) = \frac{1}{n}n\mu = \mu.$