show your work, it doesn't need graph, or some other material, you just need to proof the summation operators

Assume nx = Etix; and ny = Et=1yi 1. If Er- xi = a, then show that nx - a = 0 2. If =En=1 n En (xi - x)2 = b2, then show Er=1x 2 -nx2 = nb2 3. If axi = a2 for all 'i', then show Ztaxi = na2 4. Show that Et-1(xi - x) (yi - y) = Et=1xiyi - nxy