Two independent variables X∼N(0,1)X \sim N(0, 1)X∼N(0,1) and Y∼N(0,4)Y \sim N(0, 4)Y∼N(0,4). What is the distribution of Z=X+YZ = X+YZ=X+Y?
N(0, 3)
N(0, 5)
N(0, 9)
N(0, 2)