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- Summary
- Question on problem 7 on July Challenge

Trying to follow and learn from the solution and did not want to clutter up the original thread

Where you are swapping the expectation of a function for applying the function to the expectation which according to the inequality, the two expressions are equal only if the function is linear, which W^2 is not

My naive question is why doesn't Jensen's Inequality prevent this step?Fubini allows us to change order of integration, so we get

[tex]

\mathbb EX = \mathbb E \left ( \int _0^t W_s^2ds\right ) = \int _0^t \mathbb E(W_s^2)ds = \int_0^t sds = \frac{t^2}{2}

[/tex]

Where you are swapping the expectation of a function for applying the function to the expectation which according to the inequality, the two expressions are equal only if the function is linear, which W^2 is not