An Introduction to Probability Theory and Its Applications, Volume 2Wiley, 1950 - Probabilities Vol. 2 has series: Wiley series in probability and mathematical statistics. Bibliographical footnotes. "Some books on cagnate subjects": v. 2, p. 615-616. |
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Page 29
... denote by X1 , X2 , . . . independent variables assuming the values 1 , 2 , ... , a each with probability a1 . Denote by N , the number of representations t = y1 + Y2 + + yn of t as a sum of integers y , a . By the very definition N1 ...
... denote by X1 , X2 , . . . independent variables assuming the values 1 , 2 , ... , a each with probability a1 . Denote by N , the number of representations t = y1 + Y2 + + yn of t as a sum of integers y , a . By the very definition N1 ...
Page 42
... denote by X11 , X12 , X21 , X22 the masses of the four fragments of the second generation , the subscript 1 referring to the smaller and 2 to the larger part . Find the densities and expecta- tions of these variables . 21. Let X1 ...
... denote by X11 , X12 , X21 , X22 the masses of the four fragments of the second generation , the subscript 1 referring to the smaller and 2 to the larger part . Find the densities and expecta- tions of these variables . 21. Let X1 ...
Page 73
... denote the density of their sum S = X1 + X2 by g . The pairs ( X1 , S ) and ( X1 , X2 ) are related by the linear ... denote by X ( 1 ) , X ( 2 ) , ... , X ( n ) the random points X1 , ... , X , rearranged in increasing order . These ...
... denote the density of their sum S = X1 + X2 by g . The pairs ( X1 , S ) and ( X1 , X2 ) are related by the linear ... denote by X ( 1 ) , X ( 2 ) , ... , X ( n ) the random points X1 , ... , X , rearranged in increasing order . These ...
Contents
CHAPTER | 1 |
SPECIAL DENSITIES RANDOMIZATION | 44 |
PROBABILITY MEASURES AND SPACES | 101 |
Copyright | |
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An Introduction to Probability Theory and Its Applications, Volume 2 William Feller Limited preview - 1991 |
Common terms and phrases
a₁ applies arbitrary argument assume asymptotic atoms backward equation Baire functions Borel sets bounded central limit theorem characteristic function common distribution compound Poisson condition consider constant continuous function convergence convolution defined definition denote density derived distribution F distribution function equals example exists exponential distribution F{dx finite interval fixed follows formula given hence implies independent random variables inequality infinitely divisible integral integrand Laplace transform law of large left side lemma Let F limit distribution Markov martingale measure mutually independent normal distribution notation o-algebra obvious operator parameter Poisson process positive probabilistic probability distribution problem proof prove random walk renewal epochs renewal equation renewal process S₁ sample space satisfies semi-group sequence shows solution stable distributions stochastic stochastic kernel symmetric T₁ tends theory transition probabilities uniformly unique variance vector X₁ Y₁ zero expectation