So I have this problem that says $W,X,Y$, and $Z$ are all independent random variables and all have standard normal distribution. Find $P(W+X>Y+Z+1)$. Now I know that $W+X-Y-Z$ will also be independent and standard normal distribution, however what I'm confused about is this:
I know that if I make $W$ and $X$ standard normal I could say to let $U=W+X$ and then $U\sim N(\mu_W +\mu_X , \sigma^2_W +\sigma^2_X)$.
Now lets say I want to find $P(W+X-Y-Z>1)$ .
How would I normalize that (is that the correct verbage)? Would I say to let $V=W+X-Y-Z$ and then $V\sim N\left(\mu_W +\mu_X-\mu_Y-\mu_z , \sigma^2_W +\sigma^2_X-\sigma^2_Y-\sigma^2_Z\right)$?