$I(t)=\int_0^t \sqrt sdW_s$
What is $E(I(t)^4)$
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$I(t)=\int_0^t \sqrt tdW_s=\sqrt t \int_0^t dW_s =\sqrt t W_t $ and then $$E(I(t)^4)=E(t^2 W_t^4)=t^2 \cdot 3t^2=3t^4$$ using the 4th moment of the $N(0,\sigma^2=t)$ distribution.