I was given X~N(1,3) and Y~N(5,7) and for E[X+Y]= E[X]+E[Y], I just added the 1 and 5 and got the answer correct, but when I subtracted it for E[X-Y] I didn't get the correct answer.
I was lost thinking if E[X-Y] = E[X]-E[Y] does not exist. Can I get help on what E[X-Y] means?
Expectation is a linear operator. Just rewrite your expression as $Z=X+(-1)\cdot Y$, hence the expectation of $Z, \mathbf{E}Z = \mathbf{E}X + (-1) \cdot \mathbf{E}Y = 1+(-1)\cdot 5=-4 $