Elementary Probability for Applications 1st Edition by Rick Durrett – Ebook PDF Instant Download/Delivery: 0521867568, 978-0521867566
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ISBN 10: 0521867568
ISBN 13: 978-0521867566
Author: Rick Durrett
This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author’s philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management.
Elementary Probability for Applications 1st Table of contents:
1. Basic Concepts
1.1 Outcomes, events, and probability
1.2 Flipping coins and the World Series
1.3 Independence
1.4 Random variables and distributions
1.5 Expected value
1.6 Moments and variance
1.7 Exercises
2. Combinatorial Probability
2.1 Permutations and combinations
2.2 Binomial and multinomial distributions
2.3 Poisson approximation to the binomial
2.4 Card games and other urn problems
2.5 Probabilities of unions, Joe DiMaggio
2.6 Blackjack
2.7 Exercises
3. Conditional Probability
3.1 Definition
3.2 Two-stage experiments
3.3 Bayes’ formula
3.4 Discrete joint distributions
3.5 Exercises
4. Markov Chains
4.1 Definitions and examples
4.2 Multistep transition probabilities
4.3 Stationary distributions
4.4 Limit behavior
4.5 Gambler’s ruin
4.6 Absorbing chains
4.7 Exercises
5. Continuous Distributions
5.1 Density functions
5.2 Distribution functions
5.3 Functions of random variables
5.4 Joint distributions
5.5 Marginal and conditional distributions
5.6 Exercises
6. Limit Theorems
6.1 Sums of independent random variables
6.2 Mean and variance of sums
6.3 Laws of large numbers
6.4 Normal distribution
6.5 Central limit theorem
6.6 Applications to statistics
6.7 Exercises
7. Option Pricing
7.1 Discrete time
7.2 Continuous time
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