Need help confirming this concept. The question is asking for the Expected Value of X, E[X]. See Screenshot

• I tried to work it out myself and got a little stuck...I also included a screenshot of what I did so far. Please let me know if I'm on the right track

\fGiven an iid sample, {X1,...,X,,}, the geometric mean is dened as, G={X1-X2-....Xn)lf\" Another way of writing this is, a = (:11) Notice that the II is similar to E; but, rather than adding each of the terms in the series, instead you are multiplying each of the terms in the series. In this exercise, you will show that the geometric mean is not a consistent estimator for E[X]. Because you are proving that the geometric mean is not, in general, a consistent estimator for the expected value, you need only ElilDW that for one probability distribution this is not the case. A distribution that is easy to work 1with that will prove this point is a uniform distribution. And so, suppose that X has a uniform distribution on [i], 1]. a. [3 points] What is the expected value of X, E[X]