Hi there, I'm just going through the statement: "The population mean is equal to the expected value of the mean of sample distribution of means taken from a population"

So I've been going through the following proof:

Let X1, X2, X3, ..., Xn be a simple random sample from a population with mean μ.

E(Xbar)

= E(1/n ∑ Xi)

= 1/n * E(∑Xi)

expectation is a linear operator so we can take the sum out side of the argurement

= 1/n * ∑ E(Xi)

there are n terms in the sum and the E(Xi) is the same for all i

= 1/n * nE(Xi)

= E(Xi)

E(Xbar) = μ

I cannot for the life of me figure out how E(Xi) = μ

Would someone kindly shine some light on this!!!

Many many thanks!