Solution
= Solution
Fubini gives $\mathbb EI_t=0$. For $s\leq t$,
$$
\boxed{\mathbb E(I_sI_t)=\int_0^s\int_0^t\min(u,v)dvdu
=\int_0^s\left(ut-\frac{u^2}{2}\right)du
=\frac{s^2(3t-s)}6.}
$$
= Solution
Fubini gives $\mathbb EI_t=0$. For $s\leq t$,
$$
\boxed{\mathbb E(I_sI_t)=\int_0^s\int_0^t\min(u,v)dvdu
=\int_0^s\left(ut-\frac{u^2}{2}\right)du
=\frac{s^2(3t-s)}6.}
$$