Probability
This book is a text at the introductory graduate level, for use in the one semester or twoquarter probability course for firstyear graduate students that seems ubiquitous in departments of statistics, biostatistics, mathemat ical sciences, applied mathematics and mathematics. While it is accessi...
Main Author:  

Format:  eBook 
Language:  English 
Published: 
New York, NY
Springer New York
1993, 1993

Edition:  1st ed. 1993 
Series:  Springer Texts in Statistics

Subjects:  
Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 8 Prediction and Conditional Expectation
 8.1 Prediction in L2
 8.2 Conditional Expectation Given a Finite Set of Random Variables
 8.3 Conditional Expectation for X?L2
 8.4 Positive and Integrable Random Variables
 8.5 Conditional Distributions
 8.6 Computational Techniques
 8.7 Complements
 8.8 Exercises
 9 Martingales
 9.1 Fundamentals
 9.2 Stopping Times
 9.3 Optional Sampling Theorems
 9.4 Martingale Convergence Theorems
 9.5 Applications of Convergence Theorems
 9.6 Complements
 9.7 Exercises
 A Notation
 B Named Objects
 4.2 Integrals with respect to Distribution Functions
 4.3 Computation of Expectations
 4.4 LP Spaces and Inequalities
 4.5 Moments
 4.6 Complements
 4.7 Exercises
 5 Convergence of Sequences of Random Variables
 5.1 Modes of Convergence
 5.2 Relationships Among the Modes
 5.3 Convergence under Transformations
 5.4 Convergence of Random Vectors
 5.5 Limit Theorems for Bernoulli Summands
 5.6 Complements
 5.7 Exercises
 6 Characteristic Functions
 6.1 Definition and Basic Properties
 6.2 Inversion and Uniqueness Theorems
 6.3 Moments and Taylor Expansions
 6.4 Continuity Theorems and Applications
 6.5 Other Transforms
 6.6 Complements
 6.7 Exercises
 7 Classical Limit Theorems
 7.1 Series of Independent Random Variables
 7.2 The Strong Law of Large Numbers
 7.3 The Central Limit Theorem
 7.4 The Law ofthe Iterated Logarithm
 7.5 Applications of the Limit Theorems
 7.6 Complements
 7.7 Exercises
 Prelude: Random Walks
 The Model
 Issues and Approaches
 Functional of the Random Walk
 Limit Theorems
 Summary
 1 Probability
 1.1 Random Experiments and Sample Spaces
 1.2 Events and Classes of Sets
 1.3 Probabilities and Probability Spaces
 1.4 Probabilities on R
 1.5 Conditional Probability Given a Set
 1.6 Complements
 1.7 Exercises
 2 Random Variables
 2.1 Fundamentals
 2.2 Combining Random Variables
 2.3 Distributions and Distribution Functions
 2.4 Key Random Variables and Distributions
 2.5 Transformation Theory
 2.6 Random Variables with Prescribed Distributions
 2.7 Complements
 2.8 Exercises
 3 Independence
 3.1 Independent Random Variables
 3.2 Functions of Independent Random Variables
 3.3 Constructing Independent Random Variables
 3.4 Independent Events
 3.5 Occupancy Models
 3.6 Bernoulli and Poisson Processes
 3.7 Complements
 3.8 Exercises
 4 Expectation
 4.1 Definition and Fundamental Properties