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 7
... independent variables with densities f , g , h . The fact that summation is commutative and associative implies the same properties for convolutions , and so f * g * h is independent of the order of the operations . Positive random ...
... independent variables with densities f , g , h . The fact that summation is commutative and associative implies the same properties for convolutions , and so f * g * h is independent of the order of the operations . Positive random ...
Page 37
... random variables in simple applications . Furthermore , the uniform distribution will appear in a new light . · 1 , ... , n Let X1 , X , stand for mutually independent random variables with a common continuous distribution F. The ...
... random variables in simple applications . Furthermore , the uniform distribution will appear in a new light . · 1 , ... , n Let X1 , X , stand for mutually independent random variables with a common continuous distribution F. The ...
Page 132
William Feller. in terms of the distribution function G of u . The two definitions are equivalent by the very definition of the former integral by the approximating sums IV , ( 4.6 ) . The point is that the expectation of a random variable ...
William Feller. in terms of the distribution function G of u . The two definitions are equivalent by the very definition of the former integral by the approximating sums IV , ( 4.6 ) . The point is that the expectation of a random variable ...
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