Probability Essentials /
This introduction to Probability Theory can be used, at the beginning graduate level, for a one-semester course on Probability Theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in rela...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
2000.
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| Series: | Universitext,
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Introduction
- Axioms of Probability
- Conditional Probability and Independence
- Probabilities on a Countable Space
- Random Variables on a Countable Space
- Construction of a Probability Measure
- Construction of a Probability Measure on R
- Random Variables
- Integration with Respect to a Probability Measure
- Independent Random Variables
- Probability Distributions on R
- Probability Distributions on Rn
- Characteristic Functions
- Properties of Characteristic Functions
- Sums of Independent Random Variables
- Gaussian Random Variables (The Normal and the Multivariate Normal Distributions)
- Convergence of Random Variables; Weak Convergence
- Weak Convergence and Characteristic Functions
- The Laws of Large Numbers
- The Central Limit Theorem
- L2 and Hilbert Spaces
- Conditional Expectation
- Martingales
- Supermartingales and Submartingales
- Martingale Inequalities
- Martingale Convergence Theorems
- The Radon-Nikodym Theorem.