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Powers of Brownian motion · Part 4 of 4

$W_t$ is a standard Brownian motion started at $W_0 = 0$ . Each part asks about a function of it.

Using the Itô isometry, what is the second moment of the stochastic integral $\int_0^2 W_s\,dW_s$ ?

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Itô’s lemma and the computations you will be asked for

Using the Itô isometry, what is the second moment of the stochastic integral ∫02Ws dWs\int_0^2 W_s\,dW_s∫02​Ws​dWs​?

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Using the Itô isometry, what is the second moment of the stochastic integral $\int_0^2 W_s\,dW_s$ ?