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 156
... distribution in B and for fixed B a continuous function in x . Then ( 9.8 ) ... concentrated on two atoms . ( c ) Random sums . Let X1 , X2 , ... be ... distribution G concentrated on the points 0 , + h , .... Letting h tone convergence ...
... distribution in B and for fixed B a continuous function in x . Then ( 9.8 ) ... concentrated on two atoms . ( c ) Random sums . Let X1 , X2 , ... be ... distribution G concentrated on the points 0 , + h , .... Letting h tone convergence ...
Page 413
... distribution concentrated at μ , and so the distribution of [ X , ++ X ] / n tends to this limit . This is the weak law of large numbers in the Khintchine version , which does not require the existence of a variance . True , the proof ...
... distribution concentrated at μ , and so the distribution of [ X , ++ X ] / n tends to this limit . This is the weak law of large numbers in the Khintchine version , which does not require the existence of a variance . True , the proof ...
Page 424
... distributions concentrated on 0 , ∞o and give a complete characterization of their domains of attraction . The proofs are straight- forward and of remarkable simplicity when compared with the methods required for distributions not ...
... distributions concentrated on 0 , ∞o and give a complete characterization of their domains of attraction . The proofs are straight- forward and of remarkable simplicity when compared with the methods required for distributions not ...
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