Let g ∗ 1 (y1) = IE [g(Y1,... ,Yp)|Y1 = y1] , y1 ∈ R. Then show that IE [g(x)] = IE [g ∗ (Y)] = IE [g ∗ 1 (Y1)] = Z g ∗ 1 (y) 1 √ 2π exp µ − 1 2 (y − ξ1) 2 ¶ dy. Hence, or otherwise, provide an...

Let g ∗ 1 (y1) = IE [g(Y1,... ,Yp)|Y1 = y1] , y1 ∈ R. Then show that IE [g(x)] = IE [g ∗ (Y)] = IE [g ∗ 1 (Y1)] = Z g ∗ 1 (y) 1 √ 2π exp µ − 1 2 (y − ξ1) 2 ¶ dy. Hence, or otherwise, provide an alternative derivation of the Stein identity (Lemma 8.2).