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(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(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!