1. Let X be G-measurable and let Y be independent of G. Let f(x, y) be a bounded continuous function and define g(x) = E[f(x,Y)]. Show that E[f (X,Y)| G] = g(X). prove it when X is discrete and X is not discrete.

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A: See the detailed solution below.

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A: Yes true.

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A: As per our guidelines we can answer only 3 subparts. please ask others seperately.

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