(a) Suppose that G is the o-algebra generated by a random variable Y taking only finitely many values, i.e. G= o(Y) and Y(w) E {y,..., yn} for all w N. Show that n E[X|9] =EXY = y]1[y=y} P-a.s. i=1 (b) Give an example showing that in general, for H another -algebra on N, E[E[X|H|G] # E[X|HnG].