Suppose XXX and YYY are random variables. Under what specific condition is E[X+Y]=E[X]+E[Y]E[X + Y] = E[X] + E[Y]E[X+Y]=E[X]+E[Y]?
Only if XXX and YYY are independent.
Only if XXX and YYY have the same distribution.
Only if XXX and YYY have finite variance.
Always, by the linearity of expectation.