First Course in Probability, A, 10th edition
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Overview
A First Course in Probability explores the mathematics and potential applications of probability theory. It is an elementary introduction to the theory of probability for upperlevel and graduate students majoring in mathematics, statistics, engineering and the sciences. Through clear and intuitive explanations, it presents not only the mathematics of probability theory but also the many diverse possible applications of this subject using numerous examples. The 10th Edition includes many new and updated problems; new material on topics including the Pareto distribution, Poisson limit results, and the Lorenz curve; new examples such as computing NCAA basketball tournament win probabilities and the friendship paradox; revised and streamlined exposition for clarity and deeper understanding; and much more.
Published by Pearson (January 2nd 2023)  Copyright © 2024
ISBN13: 9780138027889
Subject: Advanced Statistics
Category: Probability & Statistics
Overview
1. Combinatorial Analysis
 1.1 Introduction
 1.2 The Basic Principle of Counting
 1.3 Permutations
 1.4 Combinations
 1.5 Multinomial Coefficients
 1.6 The Number of Integer Solutions of Equations
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
2. Axioms of Probability
 2.1 Introduction
 2.2 Sample Space and Events
 2.3 Axioms of Probability
 2.4 Some Simple Propositions
 2.5 Sample Spaces Having Equally Likely Outcomes
 2.6 Probability as a Continuous Set Function
 2.7 Probability as a Measure of Belief
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
3. Conditional Probability and Inference
 3.1 Introduction
 3.2 Conditional Probabilities
 3.3 Bayes's Formula
 3.4 Independent Events
 3.5 P(·F) Is a Probability
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
4. Random Variables
 4.1 Random Variables
 4.2 Discrete Random Variables
 4.3 Expected Value
 4.4 Expectation of a Function of a Random Variable
 4.5 Variance
 4.6 The Bernoulli and Binomial Random Variables
 4.7 The Poisson Random Variable
 4.8 Other Discrete Probability Distributions
 4.9 Expected Value of Sums of Random Variables
 4.10 Properties of the Cumulative Distribution Function
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
5. Continuous Random Variables
 5.1 Introduction
 5.2 Expectation and Variance of Continuous Random Variables
 5.3 The Uniform Random Variable
 5.4 Normal Random Variables
 5.5 Exponential Random Variables
 5.6 Other Continuous Distributions
 5.7 The Distribution of a Function of a Random Variable
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
6. Jointly Distributed Random Variables
 6.1 Joint Distribution Functions
 6.2 Independent Random Variables
 6.3 Sums of Independent Random Variables
 6.4 Conditional Distributions: Discrete Case
 6.5 Conditional Distributions: Continuous Case
 6.6 Order Statistics
 6.7 Joint Probability Distribution of Functions of Random Variables
 6.8 Exchangeable Random Variables
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
7. Properties of Expectation
 7.1 Introduction
 7.2 Expectation of Sums of Random Variables
 7.3 Moments of the Number of Events that Occur
 7.4 Covariance, Variance of Sums, and Correlations
 7.5 Conditional Expectation
 7.6 Conditional Expectation and Prediction
 7.7 Moment Generating Functions
 7.8 Additional Properties of Normal Random Variables
 7.9 General Definition of Expectation
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
8. Limit Theorems
 8.1 Introduction
 8.2 Chebyshev's Inequality and the Weak Law of Large Numbers
 8.3 The Central Limit Theorem
 8.4 The Strong Law of Large Numbers
 8.5 Other Inequalities and a Poisson Limit Result
 8.6 Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson Random Variable
 8.7 The Lorenz Curve
 Summary
 Problems
 Theoretical Exercises
 SelfTest Problems and Exercises
9. Additional Topics in Probability
 9.1 The Poisson Process
 9.2 Markov Chains
 9.3 Surprise, Uncertainty, and Entropy
 9.4 Coding Theory and Entropy
 Summary
 Problems and Theoretical Exercises
 SelfTest Problems and Exercises
10. Simulation
 10.1 Introduction
 10.2 General Techniques for Simulating Continuous Random Variables
 10.3 Simulating from Discrete Distributions
 10.4 Variance Reduction Techniques
 Summary
 Problems
 SelfTest Problems and Exercises
Answers to Selected Problems
Solutions to SelfTest Problems and Exercises
Index
Common Discrete Distributions
Common Continuous Distributions
Your questions answered
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