Correlated Brownian Motion

Hi, I have problems with the following question:

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

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

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