Suppose that an ordinary deck of 52 playing cards will be randomly ordered, and then the cards will be flipped over and observed, one after another. LettingXbe the number of cards observedpriorto observing a black ace, give the value ofE(X). (Hint: Imagine labeling the 50 cards which are not black aces from 1 to 50, and letIjbe an indicator random variable which equals 1 if thejth card which is not a black ace is observed before either of the two black aces are observed, and equals 0 otherwise. Then expressXas a sum of such indicator random variables.)