Let $\{B(t);t≥0\}$ be a Wiener process (Brownian motion) with $\sigma^2=1$. Define the stochastic process Let $\{X(t); t>0\}$ by
$X(t)=e^{-t}B(e^{2t})$
Let $Y=X(1/2)-X(0)$, and $Z=X(1)-X(1/2)$.
I am tasked to find the correlation coefficient, and among other things i need to find $E(YZ)$, which I don't know how to do. I know that $E(Y)=E(Z)=0$, and I understand how to find $E(Y^2)$ and $E(Z^2)$ by using
$V(Y)=E(Y^2)-E(Y)^2=E(Y^2)$,
and
$V(X(1/2)-X(0))=V(X(1/2))+V(X(0))-2C(X(1/2),X(0))$, and vice versa for $V(Z)$, but I can't seem to understand how to find $E(YZ)$ specifically. Can anyone help me?