From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.
From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.
Santosh S. Venkatesh is an Associate Professor of Electrical and Systems Engineering at the University of Pennsylvania, whose research interests include probability, information, communication and learning theory, pattern recognition, computational neuroscience, epidemiology and computer security. He is a member of the David Mahoney Institute for Neurological Sciences and has been awarded the Lindback Award for Distinguished Teaching.
Inhaltsangabe
Part I. Elements: 1. Probability spaces 2. Conditional probability 3. A first look at independence 4. Probability sieves 5. Numbers play a game of chance 6. The normal law 7. Probabilities on the real line 8. The Bernoulli schema 9. The essence of randomness 10. The coda of the normal Part II. Foundations: 11. Distribution functions and measure 12. Random variables 13. Great expectations 14. Variations on a theme of integration 15. Laplace transforms 16. The law of large numbers 17. From inequalities to concentration 18. Poisson approximation 19. Convergence in law, selection theorems 20. Normal approximation Part III. Appendices: 21. Sequences, functions, spaces.
Part I. Elements: 1. Probability spaces 2. Conditional probability 3. A first look at independence 4. Probability sieves 5. Numbers play a game of chance 6. The normal law 7. Probabilities on the real line 8. The Bernoulli schema 9. The essence of randomness 10. The coda of the normal Part II. Foundations: 11. Distribution functions and measure 12. Random variables 13. Great expectations 14. Variations on a theme of integration 15. Laplace transforms 16. The law of large numbers 17. From inequalities to concentration 18. Poisson approximation 19. Convergence in law, selection theorems 20. Normal approximation Part III. Appendices: 21. Sequences, functions, spaces.
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