pV[x_] := 1 - DF[x]
 
DF[x_] := If[x < 0, 1 - f1[-x], f1[x]]
 
f1[x_] := 1 + Sqrt[x/(2*Pi)]*Exp[-x/8] + (3/2)*Exp[x]*
      \[CapitalPsi][-3*(Sqrt[x]/2)] - ((x + 5)/2)*\[CapitalPsi][-(Sqrt[x]/2)]
 
\[CapitalPsi][x_] := CDF[nr, x]
 
CDF /: CDF::usage = "CDF[distribution, x] gives the cumulative distribution \
function of the specified statistical distribution evaluated at x.  For \
continuous distributions, this is defined as the integral of the probability \
density function from the lowest value in the domain to x.  For discrete \
distributions, this is defined as the sum of the probability density function \
from the lowest value in the domain to x."
 
nr = NormalDistribution[0, 1]
