Is Y defined to be the random variable X1 + X2? What is Y2? P( X1 +X2 =Y) makes no sense, you cannot have the probability of a random variable being equal to another random variable.

Please post the question exactly as it is writen from wherever you got it from.

Note: Yes, the random variable Y = X1 + X2 does follow a triangular distribution. Its pdf is equal to y if , 2 - y if and zero otherwise.