I"m not really sure how to go about this problem, so any help would be greatly appreciated!
Let X and Y be independent random variables with the same distribution, taking values 0 and 1 with equal probability. Show that
E((X+Y)(|X-Y|)) = E(X+Y)E(|X+Y|), but that X+Y and |X-Y| are not independent.
(Here, E is the expectation)