Hello,

Well, the elements of the covariance matrix are the covariances...

So we have cov(X,Y)=cov(Y,X)=.5

And finding cov(Z1,Z2) is then easy, using the fact that the covariance is a bilinear form (cov(ax,y)=a*cov(x,y) , cov(x+y,z)=cov(x,z)+cov(y,z))

Otherwise, you can note that :

Let's denote

And we know that will follow a normal distribution

See a proof in the attached pdf