Preface 

ix  
PART I PROBABILITY AND RANDOM VARIABLES 

1  (370) 

The Meaning of Probability 


3  (12) 





Probability and Induction 



Causality Versus Randomness 



The Axioms of Probability 


15  (31) 










46  (26) 





Bernoulli's Theorem and Games of Chance 





The Concept of a Random Variable 


72  (51) 



Distribution and Density Functions 



Specific Random Variables 



Conditional Distributions 



Asymptotic Approximations for Binomial Random Variable 





Functions of One Random Variable 


123  (46) 














169  (74) 



One Function of Two Random Variables 



Two Functions of Two Random Variables 





Joint Characteristic Functions 



Conditional Distributions 



Conditional Expected Values 





Sequences of Random Variables 


243  (60) 



Conditional Densities, Characteristic Functions, and Normality 





Stochastic Convergence and Limit Theorems 



Random Numbers: Meaning and Generation 






303  (68) 










PART II STOCHASTIC PROCESSES 

371  (464) 


373  (62) 



Systems with Stochastic Inputs 







Continuity, Differentiation, Integration 



Shift Operators and Stationary Processes 





Random Walks and Other Applications 


435  (64) 



Poisson Points and Shot Noise 





Cyclostationary Processes 



Bandlimited Processes and Sampling Theory 



Deterministic Signals in Noise 



Bispectra and System Identification 





The Schwarz Inequality Problems 




499  (24) 

Factorization and Innovations 



FiniteOrder Systems and State Variables 



Fourier Series and KarhunenLoeve Expansions 



Spectral Representation of Random Processes 






523  (57) 





Extrapolation and System Identification 



The General Class of Extrapolating Spectra and Youla's Parametrization 










580  (49) 












629  (66) 





Random Variables and Stochastic Processes 



The Maximum Entropy Method 










695  (78) 



Higher Transition Probabilities and the ChapmanKolmogorov Equation 





Stationary Distributions and Limiting Probabilities 



Transient States and Absorption Probabilities 





Mixed Type Population of Constant Size 



Structure of Periodic Chains 





Markov Processes and Queueing Theory 


773  (62) 










Bibliography 

835  (2) 
Index 

837  