Further check of the approximated formulae

Finally, we have checked the validity of the approximated formulae ()-() to evaluate the expected value and the standard uncertainty of $f_P$ in all cases considered in Figs.  -. The agreement is indeed excellent, even in the cases of $p=0$ of Fig. , characterized by skewed distributions. The R script to reproduce all numbers of all three figures is provided in Appendix B.7.