Y can be represented as the inverse gpower transformation of a truncated normal variable X: Y=gpower−1X,p=pX+11/p−pX+1−1/p2ifp≠0eX−e−X2ifp=0 now, the expectation of Yn can be expressed for p≠0 as EYn=EpX+11/p−pX+1−1/p2n=12nK2πσ2∫−1/p∞px+11/p−px+1−1/pnexp−12x−μXσ2dx. ☐