Abstract
This chapter discusses the parameters of distribution functions. The methods of analysis of experimental data and determining from them the probabilities of events and characteristics of random variables are given by mathematical statistics representing an extensive part of modern probability theory. The main problems of mathematical statistics consist in the development of the methods for finding estimates and researching the accuracy of their approximation to estimated characteristics and the development of the methods for testing hypotheses. A sequence of random variables {Sn} is called convergent in mean square to a random variable S if M |Sn – S|2 → 0 as n → ∞. This definition refers both to scalar and finite-dimensional vector random variables. It is easy to see that any sequence of random variables {Sn} convergent almost surely to S converges also to S in probability. The necessary and sufficient condition for the mean square convergence of a sequence {Sn} to S is the convergence of the sequence of the expectations {MSn} to MS and the convergence of the sequence of the variances of differences Sn —S to zero.
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