We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. If we assume that E(X+Y) exists, could we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)