Let x be equal to 1 or 0 depending on whether the ball

Question

An urn contains 12 balls, of which 8 are white and 4 are black. A ball is drawn and its color noted. The ball drawn is then replaced; at the same time 2 balls of the same color as the ball drawn are added to the urn. The process is repeated until 5 balls have been drawn. For j = 1,2, ... , 5 let X; be equal to 1 or 0, depending on whether the ball drawn on the jth draw is white or black. Find E[X₂], a²[X₂], Cov [X_1, X₂].