/*   10-05  10-03-2023  2 other estimators mathematica expectation R(f')   */

     /* BCV 2 */

fx = f0 + x f1 + x^2 f2 /2 + x^3 f3/6 + x^4 f4 /24

pM = Integrate[ fx,{x,-3h/2,-h/2}]
p0 = Integrate[ fx,{x, -h/2, h/2}]
pP = Integrate[ fx,{x,  h/2,3h/2}]


fhat2 = ( v2 - v0 ) / ( 2 n h )

ev = Expand[ 1/(4n^2h^3) * ( n pP(1-pP) + (n pP)^2 + n pM(1-pM) + (n pM)^2 - 2(-n pP pM + n^2 pP pM) ) ]