Correlated Brownian Motion

Hi, I have problems with the following question:

If $\displaystyle W_t$ and $\displaystyle Z_t$ are correlated Wiener processes with instantaneous correlation $\displaystyle \rho$, find the mean and variance of $\displaystyle Y_t$, where

$\displaystyle Y_t$ = $\displaystyle \displaystyle\int^t_0 s*W_s\,dZ_s$

I got the mean=0 and variance = $\displaystyle t^4/4$, it seems a bit wired to me that the variance does not contain $\displaystyle \rho$, not sure if I did something wrong, any comments?