To the proof of the Gauss formula for the normal distribution density of continuous random variables

Lviv Polytechnic National University

Four properties of random errors of intent are given. Three known integral conditions for dispersion, mathematical expectation and random error distribution density are recorded. An integral condition is added to them for the derivative of the density of the distribution. On the basis of all these conditions and the properties of random errors, a differential equation for the density of the normal distribution and its solution are obtained.