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 37
... distribution F. The probability that any two variables assume the same value is zero , and we can therefore restrict ... DISTRIBUTIONS Empirical Distributions.
... distribution F. The probability that any two variables assume the same value is zero , and we can therefore restrict ... DISTRIBUTIONS Empirical Distributions.
Page 146
... distribution . Denote the contributions of the even and odd terms by U and V , respectively . Obviously U and V are ... F we shall denote the distribution of -X by -F . At points of continuity we have ( 5.1 ) -F ( x ) = 1 − F ( —x ) ...
... distribution . Denote the contributions of the even and odd terms by U and V , respectively . Obviously U and V are ... F we shall denote the distribution of -X by -F . At points of continuity we have ( 5.1 ) -F ( x ) = 1 − F ( —x ) ...
Page 163
... distribution in - h , h [ see II , 4 ( b ) ] . Then F ☆ U and F ☆ T have the densities • h - h1 [ F ( x + h ) F ( x ) ] and h2 | [ F ( x + y ) F ( x , y ) ] dy . - 8. Let F have atoms a1 , a2 , ... with weights P1 , P2 , maximum of P1 ...
... distribution in - h , h [ see II , 4 ( b ) ] . Then F ☆ U and F ☆ T have the densities • h - h1 [ F ( x + h ) F ( x ) ] and h2 | [ F ( x + y ) F ( x , y ) ] dy . - 8. Let F have atoms a1 , a2 , ... with weights P1 , P2 , maximum of P1 ...
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 |
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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