How do you find the mean and variance for:
$Z_{T} = \int_{0}^{T} |W_{t}|^{1/2} dW_{t}$
$Y_{T} = \int_{0}^{T} \text{sign}(W_{t}) dW_{t}$ where $\text{sign}(y) = 1$ for $y \ge 0$ and $0$ otherwise.
I'm trying to use Ito's lemma for $Z_{t}$ where $dZ_{t}= f_{t}dt + f_{x}dW_{t} + \frac{1}{2}f_{xx}dt$ but I don't know what to use for $f(t, x)$.
