I'm not sure what you mean by 2 squared
V(Y-X)=V(Y)+V(X)
Then in part 2 use D=Y-X, so you want P(D>0)
which you compute by standardizing D and using your N(0,1) tables.
Suppose X and Y are independent random variables with X ~ N(6,2square) and Y ~ N(4,4square) Put D = Y -X
(i) What is the probability distribution of D?
(ii) Using you answer to (i) above or otherwise, evaluate P(Y<X)
My answer for (i) D ~ N(-2,12)
I am not sure if its correct, so please help!