- #1

cdux

- 188

- 0

Given Theta_n = (2/n)(X1 + X2 + ... + Xn) being an unbiased estimator of Theta for a U(0,Theta), we have to prove it by showing E(Theta_n) = Theta.

And we go on E(Theta_n) = (2/n)E(X1+X2 + .. Xn)

Now at this point the solution is (2/n) * n * (Theta/2) (= Theta which is the sought-after result)

I understand that Theta/2 is the mean of a U() but how exactly does one go from E(X1 + X2 + .. Xn) to equaling it to n*E(Xi)? Is E(X1) = E(X2) = E(Xi)? If yes, why?

(PS. A more complex example is Var(X1+X2 + .. Xn) appearing to also result to nV(Xi) (=nσ^2) )