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 68
... equals the ratio of the areas of N and г. By obvious analogy with the one - dimensional situation we say that the pair ( X1 , X2 ) is distributed uniformly over г. The marginal density of X1 at the abscissa x equals the width of П at x1 ...
... equals the ratio of the areas of N and г. By obvious analogy with the one - dimensional situation we say that the pair ( X1 , X2 ) is distributed uniformly over г. The marginal density of X1 at the abscissa x equals the width of П at x1 ...
Page 74
... equals the probability that ( X1 , ... , X1 ) lies in one of the n ! replicas of A , and this probability in turn equals n ! times the volume of A. Thus P { ( X ( 1 ) , .. X ( n ) ) E A } equals the ratio of the volumes of A and of N ...
... equals the probability that ( X1 , ... , X1 ) lies in one of the n ! replicas of A , and this probability in turn equals n ! times the volume of A. Thus P { ( X ( 1 ) , .. X ( n ) ) E A } equals the ratio of the volumes of A and of N ...
Page 102
... equals ƒ on A and vanishes elsewhere . Consider now the intersection C = AB of two sets . Its indicator 1c equals 0 wherever either 14 or 1 vanishes , that is , 1c inf ( 14 , 1B ) equals the smaller of the two functions . To exploit ...
... equals ƒ on A and vanishes elsewhere . Consider now the intersection C = AB of two sets . Its indicator 1c equals 0 wherever either 14 or 1 vanishes , that is , 1c inf ( 14 , 1B ) equals the smaller of the two functions . To exploit ...
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