Question: 5. If X is an integrable random variable and & is a sub-o-field, show that E[XE(X |8)] = ENE(X|8)}2]. Let 0 = R, with the

5. If X is an integrable random variable and & is a sub-o-field, show that E[XE(X |8)] = ENE(X|8)}2]. Let 0 = R, with the Borel o-field on it. Let a probability measure P have density given by p(x) = e . Let & be the o-field generated by the finite partition P = {(-oo, -1], (-1, 0], (0, 1], (1, co) }. Let X (w) = elwl/2 for all w E 2. Calculate E(X| 6)

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