81. Sur une généralisation de la loi sinusoidale limite. Rend. Circ. Mat. Palermo, t. 57,1933, pp. 130 – 136.83. New criteria of r<strong>and</strong>omness of a series of trials. Trudy SAGU, ser. Math., No. 9, 1933,pp. 18 – 31. (R)84. On posterior probabilities. Ibidem, No. 8, pp. 18 – 32. (R)85. Sui due problemi di distribuzione casuale. GIIA, No. 2 – 3, 1935, pp. 196 – 218.86. On the newest methods of mathematical statistics applied in field experiments.Sozialistich. Nauka i Tekhnika No. 3 -4, 1934, pp. 75 – 86. (R)87. Mathematical statistics <strong>and</strong> industry. Ibidem, No. 9, pp. 1 – 14. (R)89. On the Chebyshev inequality for the bivariate case. Trudy SAGU, ser. Math., No. 11,1934, pp. 1 – 6. (R)91. Sur une formula de A.R. Crathorne. C.r., t. 200, 1935, pp. 105 – 107.92. Integration of involutory systems of any class with partial derivatives of any order.Bull. SAGU, No. 20 – 1, 1935. (R)93. Sui momenti della distribuzione ipergeometrica. GIIA, t. 6, No. 2, 1935.94. Review of Fisher, R.A. Statistical Methods for Research Workers. Sozialistich.Rekonstruktsia i Nauka, No. 9, 1935, pp. 123 – 127. (R)95. On the application of mathematical statistics <strong>and</strong> theory of probability in the industriesof the Soviet Union. J. Amer. Stat. Assoc., vol. 30, 1935, pp. 709 – 710.96. Recherches sur les chaînes de Markoff. Acta Math., t. 66, 1936, pp. 147 – 251.97. The meaning <strong>and</strong> the power of statistical criteria. Sozialistich. Rekonstruktsia i Nauka,No. 3, 1936, pp. 84 – 89. (R)98. On a method of industrial control. Problemy Ucheta i Statistiki, vol. 2, No. 2, 1936, pp.3 – 13. (R)99. Note on the method of moments. Biometrika, vol. 28, 1936, pp. 188 – 190.100. Review of Fisher, R.A. Design of Experiments. Sozialistich. Nauka i Tekhnika, No. 7,1936, pp. 123 – 125. (R)104. On a new method of solving some linear finite equations with two independentvariables. MS, vol. 3(45), No. 1, 1938, pp. 144 – 165. (R)105. 9 (Mathematical <strong>Statistics</strong>): M. – L., 1938.106. Analytical inequalities <strong>and</strong> statistical tests. Izvestia AN, ser. Math., No. 4, 1938, pp.457 – 474. (R)107. Quelques problèmes nouveaux de la théorie des chaînes de Markoff. Conf. Intern. Sci.Math. Genevé 1938. Paris, 1938, No. 4, pp. 43 – 66.108. Mathematical statistics. Bolshaia Sovetskaia Enziklopedia (Great Sov. Enc.), vol. 38,1938, pp. 406 – 410.109. Least squares, method of. Ibidem, vol. 41, 1939, pp. 53 – 56.111. Mathematical research in Uzbekistan during 15 years. In ; 6 15 (Science in Uzbekistan during 15 years). Tashkent, 1939, pp. 49 – 52.112. 8 0 0 (On Chain Correlations). Tashkent, 1939.113. On analysis of variance. Trudy sektora matematiki Komiteta Nauk Uzbek Republic,No. 1, 1939, pp. 3 – 12. (R)114. (Elementary Course inMathematical <strong>Statistics</strong>). M. – L., 1939.115. 9 (Statistical ProblemsConnected with Markov Chains). Tashkent, 1940.116. On inductive conclusions in statistics. Trudy Uzbek Filial AN, ser. 4, math., No. 3,1942, pp. 3 – 22. (R)117. Chain connections <strong>and</strong> tests of r<strong>and</strong>omness. Izvestia Uzbek Filial AN, No. 7, 1940,pp. 38 – 50. (R)
119. On the Markov method of establishing limit theorems for chain processes. Ibidem,No. 3, 1941, pp. 3 – 8. (R)120. The main concepts <strong>and</strong> problems of mathematical statistics. Trudy Uzbek Filial AN,ser. Math., No. 2, 1941, pp. 3 – 23. (R)121. Bicyclic chains. Ibidem, No. 1, 1941, pp. 3 – 41. (R)122. Same title as [116]. Ibidem, No. 3, 1942. (R)123. On the main aims of the theory of errors. Ibidem, No. 4, 1943. (R)124. On a case of chain correlation. Bull. SAGU, No. 23, 1945, pp. 17 – 18. (R)125. On the limiting distribution of sample characteristics. Ibidem (R)126. The main property of polycyclic chains. Scientific Conference SAGU. Tashkent,1945, pp. 20 – 21. (R)127. On probabilities of the repetition of cycles in polycyclic chains. Trudy SAGU, No. 7,1946. (R)129. On Markov – Bruns chains. Ibidem, No. 23, 1945, pp. 23 – 25. (R)130. On some theorems concerning the method of least squares. Doklady AN, vol. 51, No.4, 1946, pp. 259 – 262. (R)131. On the Pearson curves. Trudy IMM AN Uzbek SSR, No. 1, 1946, pp. 3 – 13. (R)132. On limiting distributions for stochastic processes with discrete time. Trudy SAGU,No. 4, 1945. (R)133. On specifying the location of a target by straddling <strong>and</strong> recording the shell bursts.Trudy IMM AN Uzbek SSR, No. 2, 1947, pp. 3 – 10. (R)134. Estimating the quality of production by progressive small samples. Ibidem, pp. 11-15. (R)135. On some problems of long-term regulation of drainage. Ibidem, pp. 126 – 27. (R)136. 2 (Application ofMathematical <strong>Statistics</strong> in Experimentation).M. – L., 1947.137. 8 (Main Goals of the Theory of Errors). M. – L.,1947.139. On estimating the successfulness of forecasting. Doklady AN Uzbek SSR, No. 8, 1948,pp. 3 – 7. (R)140. Observations of unequal weight. Ibidem, No. 1, 1949, pp. 3 – 6. (R)142. 3 9 (Discrete Markov Chains). M., 1949.143. On ordered samples from one <strong>and</strong> the same continuous population. Trudy IMM ANUzbek SSR, No. 7, 1949, pp. 5 – 17. (R)144. On the limiting distribution of relative frequencies in samples from a continuousdistribution. < , 25. 6 7 (Jubilee Coll.Articles Devoted to the 25 th Anniversary of the Uzbek SSR). Tashkent, 1949, pp. 31 – 38.(R)144a. On an implicit Markov lemma <strong>and</strong> on similar lemmas. Doklady AN Uzbek SSR, No.4, 1949, pp. 3 – 5. (R)145. On statistically checking the course of production by ordered samples. VestnikMashinostroenia, 1950. (R)146. On the distribution of a target. Artilleriisk. Zhurnal, No. 12, 1950, pp. 20 – 24. (R)147. On the best critical region for checking simple alternative hypotheses. Doklady ANUzbek SSR, No. 5, 1950, pp. 3 – 6. (R)148. On a method of double-level checking. In (Interchangeability <strong>and</strong> Checking in Machine-Building). M., 1950, pp.167 – 181. (R)149. Comparing consecutive samples from one <strong>and</strong> the same normal population by means<strong>and</strong> variances. Doklady AN Uzbek SSR, No. 3, 1951, pp. 3 – 5. (R)
- Page 3:
of All Countries and to the Entire
- Page 6 and 7:
(Coll. Works), vol. 4. N.p., 1964,
- Page 8 and 9:
individuals of the third class, the
- Page 10:
From the theoretical point of view
- Page 13 and 14:
Second case: Each crossing can repr
- Page 15 and 16:
On the other hand, for four classes
- Page 17 and 18:
f i = i S + i , i = 1, 2, 3, 4, (
- Page 19 and 20:
f 1 = C 1 P(f 1 ; …; f n+1 ), C 1
- Page 21 and 22:
ut in this case f = 2 , f 1 = 2 ,
- Page 23 and 24:
I also note the essential differenc
- Page 25 and 26:
A 1 23n1 + 1 A 1 A 1 … A 11A 2 A
- Page 27 and 28:
coefficient of 2 in the right side
- Page 29 and 30:
h(A r h - c h A r 0 ) = - A r0we tr
- Page 31 and 32:
Notes1. Our formulas obviously pres
- Page 33 and 34:
Bernstein’s standpoint regarding
- Page 35 and 36:
Corollary 1.8. A true proposition c
- Page 37 and 38:
It is important to indicate that al
- Page 39 and 40:
ut for the simultaneous realization
- Page 41 and 42:
devoid of quadratic divisors and re
- Page 43 and 44:
propositions (B i and C j ) can be
- Page 45 and 46:
A ~ A 1 and B = B 1 , we will have
- Page 47 and 48:
included in a given totality as equ
- Page 49 and 50:
For unconnected totalities we would
- Page 51 and 52:
proposition given that a second one
- Page 53 and 54:
On the other hand, let x be a parti
- Page 55 and 56:
totality is perfect, but that the j
- Page 57 and 58:
In this case, all the finite or inf
- Page 59 and 60:
probabilities p 1 , p 2 , … respe
- Page 61 and 62:
where x is determined by the inequa
- Page 63 and 64:
totality of the second type (§3.1.
- Page 65 and 66:
x = /2 + /(23) + … + /(23… p n
- Page 67 and 68:
that the fall of a given die on any
- Page 69 and 70:
infinitely many digits only dependi
- Page 71 and 72:
10. (§2.1.5). Such two proposition
- Page 73 and 74:
F(x + h) - F(x) = Mh, therefore F(x
- Page 75 and 76: “confidence” probability is bas
- Page 77 and 78: x1+ Lp n (x) x1− Lx1+ Lf(t)dt < x
- Page 79 and 80: |(x 1 ; t 0 ; t 1 ) - 1 t0tf(t)dt|
- Page 81 and 82: 5. The distribution ofξ , the arit
- Page 83 and 84: P(x 1i < x) = F(x; a i ) = C(a i )
- Page 85 and 86: egards his promises. Markov shows t
- Page 87 and 88: other solely and equally possible i
- Page 89 and 90: notion of probability and of its re
- Page 91 and 92: However, already in the beginning o
- Page 93 and 94: the revolution. My main findings we
- Page 95 and 96: Nevertheless, Slutsky is not suffic
- Page 97 and 98: path that would completely answer h
- Page 99 and 100: on political economy as well as wit
- Page 101 and 102: scientific merit. Borel was indeed
- Page 103 and 104: [3] Already in Kiev Slutsky had bee
- Page 105 and 106: different foundation. The difficult
- Page 107 and 108: 5. On the criterion of goodness of
- Page 109 and 110: --- (1999, in Russian), Slutsky: co
- Page 111 and 112: Here also, the author considers the
- Page 113 and 114: second, it is not based on assumpti
- Page 115 and 116: experimentation and connected with
- Page 117 and 118: Russian, and especially of the Sovi
- Page 119 and 120: station in England. This book, as h
- Page 121 and 122: Uspekhi Matematich. Nauk, vol. 10,
- Page 123 and 124: variety and detachment of those lat
- Page 125: 46. On the distribution of the regr
- Page 129 and 130: No lesser difficulties than those e
- Page 131 and 132: Separate spheres of work considerab
- Page 133 and 134: 10. Anderson, O. Letters to Karl Pe
- Page 135 and 136: Hier sind, im Allgemeinen, ganz ana
- Page 137 and 138: Jedenfalls, glaube ich erwiesen zu
- Page 139 and 140: werde ich das ganze Material in kur
- Page 141 and 142: considered as the limiting case of
- Page 143 and 144: and, inversely,] = m ...1 2 N[ ch h
- Page 145 and 146: µ 2 2 = m 2 2 - 2m 2 m 1 2 + m 1 4
- Page 147 and 148: (x k - x k+1 ) … (x k - x +) = E(
- Page 149 and 150: the thus obtained relations as pert
- Page 151 and 152: [1/S(S - 1)(S - 2)][(Si = 1Sx i ) 3
- Page 153 and 154: ( N −1)((S − N )(2NS− 3S− 3
- Page 155 and 156: µ 5 + 2µ 2 µ 3 = U [S/S] 5 + 2U
- Page 157 and 158: case, the same property is true wit
- Page 159 and 160: It follows that the question about
- Page 161 and 162: then expressed my doubts). And Gned
- Page 163 and 164: For Problem 1, formula (7) shows th
- Page 165 and 166: Let us calculate now, by means of f
- Page 167 and 168: ϕ′1(x)1E(a|x 1 ; x 2 ; …; x n
- Page 169 and 170: Theorem 3. If the prior density 3
- Page 171 and 172: P( ≤ ≤ |, 1 , 2 , …, s )
- Page 173 and 174: 6. A Sensible Choice of Confidence
- Page 175 and 176: 0 = A 0 n, = B2, = B2, 0 = C 0 n
- Page 177 and 178:
Note also that (95),(96), (83),(85)
- Page 179 and 180:
Γ(n / 2)Γ [( n −1) / 2]k = (1/2
- Page 181 and 182:
f (x 1 , x 2 , …, x n ) = 1 if x
- Page 183 and 184:
and the probability of achieving no
- Page 185 and 186:
E = kEµ. (14)In many particular ca
- Page 187 and 188:
a = np, b = np 2 = a 2 /n, = a/nand
- Page 189 and 190:
with number (2k - 2), we commit an
- Page 191 and 192:
(67)which is suitable even without
- Page 193 and 194:
" = 1/[1 - e - ], = - ln [1 - (1/
- Page 195 and 196:
Such structures are entirely approp
- Page 197 and 198:
11. As a result of its historical d
- Page 199 and 200:
exaggeration towards a total denial