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?