Problem 194 of 333HardStochastic CalculusP194

Mean and variance of the integral of W dW

Let $I_T = \int_0^T W_t\,dW_t$ (Itô). Find $E[I_T]$ and $\mathrm{Var}(I_T)$ . Check your variance with the Itô isometry. What is the standard deviation when $T = 2$ ?
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