Analysis of the folded normal distribution of a random variable

The analysis of the behavior of random variables after various transformations can be used in the practical solution of many non-trivial problems. In particular, solutions that cannot be expressed purely analytically, from the point of view of practical applicability, are able to give results with accuracy sufficient for real calculations, taking the inexpressible discrepancy of the analytical solution far beyond the actual error. In this paper, the behavior of the modulus of a normally distributed random variable is investigated and it is found out under what conditions it is possible to neglect the operation of taking an absolute value and approximate the modulus of a random variable with a similar probability distribution.