Using the Chebyshev inequality to find the upper estimate of the probability that the random quantity ξ, having an ensemble average mξ and variance σ 2 ξ , will deviate from mξ on value less than 3σξ....

Using the Chebyshev inequality to find the upper estimate of the probability that the random quantity ξ, having an ensemble average mξ and variance σ 2 ξ , will deviate from mξ on value less than 3σξ.

The large number n of independent trials is yielded, in each of trial we have the realization of the random variable ξ, which has a uniform distribution at

observed quantities of a random variable ξ. On the basis of the law of averages to find out, to what number a the value η will converge in probability under n → ∞. To estimate a maximum (practically possible) error of the equality η ≈ a.