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 45
... variance o2 / a2 . It follows that for each type there exists at most one density with zero expectation and unit variance . We recall from I , ( 2.12 ) that the convolution f = f1 * f2 of two densities fi and f2 is the probability ...
... variance o2 / a2 . It follows that for each type there exists at most one density with zero expectation and unit variance . We recall from I , ( 2.12 ) that the convolution f = f1 * f2 of two densities fi and f2 is the probability ...
Page 291
... variance amąt . Adding am1 reduces the expectation to zero without affecting the variance [ example ( 2.d ) ] . Thus under the stated conditions the operator A of ( 4.3 ) generates a semi - group of distributions 2 , with zero ...
... variance amąt . Adding am1 reduces the expectation to zero without affecting the variance [ example ( 2.d ) ] . Thus under the stated conditions the operator A of ( 4.3 ) generates a semi - group of distributions 2 , with zero ...
Page 359
... variance o2 the calculations are performed in 1 ; XIII , 6 . They do not depend on the arithmetic character of F and so we have the general result : If F has expectation μ and variance o2 then for large t the number N , of renewal ...
... variance o2 the calculations are performed in 1 ; XIII , 6 . They do not depend on the arithmetic character of F and so we have the general result : If F has expectation μ and variance o2 then for large t the number N , of renewal ...
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