I was just wondering, if I have two variable x and y
x~N(0,1/2) and y~i*N(0,1/2)
Then would their sum x+y ~ N(0,1/2) + iN(0,1/2)
I don't think this is true but can someone show me if I'm right/wrong.
Also if I have x*i would this have distribution i*N(0,1/2)?