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140122  eng 
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a 9781461208914

100 
1 

a Karr, Alan F.

245 
0 
0 
a Probability
h Elektronische Ressource
c by Alan F. Karr

250 


a 1st ed. 1993

260 


a New York, NY
b Springer New York
c 1993, 1993

300 


a XXI, 283 p
b online resource

505 
0 

a 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

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a 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 

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a 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 

653 


a Probability Theory

653 


a Probabilities

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0 
7 
a eng
2 ISO 6392

989 


b SBA
a Springer Book Archives 2004

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0 

a Springer Texts in Statistics

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5 
0 
a 10.1007/9781461208914

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4 
0 
u https://doi.org/10.1007/9781461208914?nosfx=y
x Verlag
3 Volltext

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0 

a 519.2

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a 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 ble to advanced ("mathematically mature") undergraduates, it could also serve, with supplementation, for a course on measuretheoretic probability. Students who master this text should be able to read the "hard" books on probability with relative ease, and to proceed to further study in statistics or stochastic processes. This is a book to teach from. It is not encyclopredic, and may not be suitable for all reference purposes. Pascal once apologized to a correspondent for having written a long letter, saying that he hadn't the time to write a short one. I have tried to write a short book, which is quite deliberately incomplete, globally and locally. Many topics, including at least one of everyone's favorites, are omitted, among them, infinite divisibility, interchangeability, large devia tions, ergodic theory and the Markov property. These can be supplied at the discretion and taste of instructors and students, or to suit particular interests
