title: Some Random Series Functions 2ed (Cambridge Studies in Advanced Mathematics)
author: Kahane
description: "...a rewarding [book], certain to have a wide influence." Robert Kaufman, American Scientist
zlib_text: 2 
   
   
   
    
  Leif Mejlbro
   
  Probability Examples c-7
  Analytic Aids
  Download free eBooks at bookboon.com
  
  3 
   
   
   
  Probability Examples c-7 – Analytic Aids 
  © 2014 Leif Mejlbro & bookboon.com 
  ISBN 978-87-7681-523-3
   
  Download free eBooks at bookboon.com
  
  Analytic Aids
   
  4 
  Contents
   
  Introduction  
  5
  1  
  Generating functions; background  
  6 
  1.1  
  Denition of the generating function of a discrete random variable   
  6 
  1.2  
  Some generating functions of random variables  
  7 
  1.3  
  Computation of moments  
  8 
  1.4  
  Distribution of sums of mutually independent random variables  
  8 
  1.5  
  Computation of probabilities  
  9 
  1.6  
  Convergence in distribution  
  9
  2  
  The Laplace transformation; background  
  10 
  2.1  
  Denition of the Laplace transformation  
  10 
  2.2  
  Some Laplace transforms of random variables  
  11 
  2.3  
  Computation of moments   
  12 
  2.4  
  Distribution of sums of mutually independent random variables  
  12 
  2.5  
  Convergence in distribution  
  13
  3  
  Characteristic functions; ba