In the bivariate situation, show that E is a linear or nondistributive operator. That is, show that E[a1u1(X1,X2)+a2u2(X1,X2)]=a1E[u1(X1,X2)]+a2E[u2(X1,X2)].
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That follows directly from the integral or sum or better yet if you express the expectation as
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