Let XXX and YYY be independent standard normal. What is the distribution of X+YX + YX+Y?
N(0,1)N(0, 1)N(0,1)
N(0,2)N(0, 2)N(0,2)
N(1,2)N(1, 2)N(1,2)
Exponential(1)\text{Exponential}(1)Exponential(1)