particles, the consequent interactions of those particles are all subject to random processes. Thus, even if the primary particles are the same and have the same primary energies $E_0$ and the same zenith angles of the incidence to the atmosphere, the shower development through it will be different.\
But it is the depth of the shower maximum, $X_{max}$, and the total number of electrons, $N(X)$, at various depths $X$ that will be different. Continuing our and other author’s work (see Section 2.1) we show that *when referred to the shower maximum depth the function describing fully the distributions of all electron characteristics is the same in any shower, independently of the primary energy, mass, angle of incidence or fluctuations of shower development*.\
By referring to the shower maximum we mean that instead of the depth $X$ one should use the age $s$ of the shower at this depth, defined as $$s(X)=3X/(X+2X_{max})    \;\textnormal{.}$$ This was introduced for a description of shower development stage by Hillas [@hillas] by analogy to a pure electromagnetic cascade where this particular relation comes out of the analytical solutions. It can be seen that the age $s$ depends actually on the ratio $X/X_{max}$, so that this very 