Let X∼N(0,1)X \sim N(0, 1)X∼N(0,1). Using Stein's Lemma or otherwise, find the expected value E[XetX]E[X e^{t X}]E[XetX].
tet2/2t e^{t^2/2}tet2/2
et2/2e^{t^2/2}et2/2
t2et2/2t^2 e^{t^2/2}t2et2/2
te−t2/2t e^{-t^2/2}te−t2/2