### Probability

This book is a text at the introductory graduate level, for use in the one­ semester or two-quarter probability course for first-year graduate students that seems ubiquitous in departments of statistics, biostatistics, mathemat­ ical sciences, applied mathematics and mathematics. While it is accessi...

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Main Author: eBook English New York, NY Springer New York 1993, 1993 1st ed. 1993 Springer Texts in Statistics Springer Book Archives -2004 - Collection details see MPG.ReNa
• 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