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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

in Russia) and the expressions normal law and coefficient **of** correlationwere likewise absent in his works. And, not wishing to leave his field(§13.3-1, letter to Chuprov), he never mentioned applications **of** his chainsto natural sciences. The structure **of** his Treatise became ever morecomplicated with each new edition.13.3. Markov: Main Investigations1) Mathematical treatment **of** observations. In spite **of** severalcommentators, I deny Markov’s accomplishments here. Neyman (1934, p.595) invented a non-existing Gauss – Markov theorem and F. N. David &Neyman (1938) repeated this mistake but finally Neyman (1938/1952, p.228) admitted it.In his Treatise (1900) Markov combined the treatment **of** observationswith the study **of** correlation, statistical series and interpolation, but hisinnovation was methodically doubtful. While discussing statistical series,Markov did not mention Chuprov’s relevant papers (1916; 1918 – 1919).When considering Weldon’s experiment with 26,306 throws **of** 12 dice (K.Pearson 1900), Markov (Treatise 1924, pp. 349 – 353) decided, afterapplying the CLT and the Bayes theorem with transition to the normal law,that the probability **of** a 5 or a 6 was higher than 1/3. Unlike Pearson, he hadnot used the chi-squared test and apparently left an impression that(although suitable for a small number **of** trials as well) it was not needed atall. Markov possibly followed here his own rigid principle (Ondar1977/1981, Letter 44 to Chuprov **of** 1910): I shall not go a step out **of** thatregion where my competence is beyond any doubt.The explication **of** the MLSq proper was involved; in a letter **of** 1910 toChuprov Markov (Ondar 1977/1981, p. 21) wrote: I have **of**ten heard thatmy presentation is not sufficiently clear. In 1893, his former student,Koialovitch (**Sheynin** 2006a, pp. 81 and 85), writing to Markov, formulatedsome puzzling questions about his university lectures.2) The LLN. Markov (1906/1951, p. 341) noted that the conditionlimE{[E∑ξ i – ∑Eξ i )] 2 /n 2 } = 0, n → ∞(1)was sufficient for the sequence ξ 1 , ξ 2 , …, ξ n , … **of** random variables to obeythe LLN; or to comply with the conditionlimP{(1/n)|(∑ξ i – ∑Eξ i )| < ε} = 1, n → ∞.Then Markov (Ibidem, pp. 342 – 344; Treatise, 1913, pp. 116 – 129)derived a few sufficient conditions for sequences **of** independent, and,especially, dependent random variables (1906/1951, p. 351; Treatise 1913,p. 119; 1924, p. 174), provided examples **of** sequences not obeying the law,and (Treatise, 1913, p. 129), proved that independent variables obeyed theLLN if, for every i, there existed the momentsEξ i = a i , E|ξ i – a i | 1+δ < C, 0 < δ < 1.Again, Markov (Treatise, 1900; p. 86 in the edition **of** 1924) had provedthat, for a positive random variable ξ,131