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Prob/Stats Probability: The Science of Uncertainty by Michael A. Bean

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  1. Jan 19, 2013 #1

    Table of Contents:
    Code (Text):

    [LIST]
    [*] Introduction
    [LIST]
    [*] What is Probability?
    [*] How is Uncertainty Quantified?
    [*] Probability in Engineering and the Sciences
    [*] What is Actuarial Science
    [*] What is Financial Engineering?
    [*] Interpretations of Probability
    [*] Probability Modeling in Practice
    [*] Outline of This Book
    [*] Chapter Summary
    [*] Further Reading
    [*] Exercises
    [/LIST]
    [*] A Survey of Some Basic Concepts Through Examples
    [LIST]
    [*] Payoff in a Simple Game
    [*] Choosing Between Payoffs
    [*] Future Lifetimes
    [*] Simple and Compound Growth
    [*] Chapter Summary
    [*] Exercises
    [/LIST]
    [*] Classical Probability
    [LIST]
    [*] The Formal Language of Classical Probability
    [*] Conditional Probability
    [*] The Law of Total Probability
    [*] Bayes' Theorem
    [*] Chapter Summary
    [*] Exercises
    [*] Appendix on Sets, Combinatorics, and Basic Probability Rules
    [/LIST]
    [*] Random Variables and Probability Distributions
    [LIST]
    [*] Definitions and Basic Properties
    [LIST]
    [*] What is a Random Variable?
    [*] What is a Probability Distribution?
    [*] Types of Distributions
    [*] Probability Mass Functions
    [*] Probability Density Functions
    [*] Mixed Distributions
    [*] Equality and Equivalence of Random Variables
    [*] Random Vectors and Bivariate Distributions
    [*] Dependence and Independence of Random Variables
    [*] The Law of Total Probability and Bayes' Theorem (Distributional Forms)
    [*] Arithmetic Operations on Random Variables
    [*] The Difference Between Sums and Mixtures
    [*] Exercises
    [/LIST]
    [*] Statistical Measures of Expectation, Variation and Risk
    [LIST]
    [*] Expectation
    [*] Deviation from Expectation
    [*] Higher Moments
    [*] Exercises
    [/LIST]
    [*] Alternative Ways of Specifying Probability Distributions
    [LIST]
    [*] Moment and Cumulant Generating Functions
    [*] Survival and Hazard Functions
    [*] Exercises
    [/LIST]
    [*] Chapter Summary
    [*] Additional Exercises
    [*] Appendix on Generalized Density Functions (Optional)
    [/LIST]
    [*] Special Discrete Distributions
    [LIST]
    [*] The Binomial Distribution
    [*] The Poisson Distribution
    [*] The Negative Binomial Distribution
    [*] The Geometric Distribution
    [*] Exercises
    [/LIST]
    [*] Special Continuous Distributions
    [LIST]
    [*] Special Continuous Distributions for Modeling Uncertain Sizes
    [LIST]
    [*] The Exponential Distribution
    [*] The Gamma Distribution
    [*] The Pareto Distribution
    [/LIST]
    [*] Special Continuous Distribution for Modeling Lifetimes
    [LIST]
    [*] The Weibull Distribution
    [*] The DeMoivre Distribution
    [/LIST]
    [*] Other Special Distributions
    [LIST]
    [*] The Normal Distribution
    [*] The Lognormal Distribution
    [*] The Beta Distribution
    [/LIST]
    [*] Exercises
    [/LIST]
    [*] Transformation of Random Variables
    [LIST]
    [*] Determining the Distribution of a Transformed Random Variable
    [*] Expectation of a Transformed Random Variable
    [*] Insurance Contracts with Caps, Deductibles and Coinsurance (Optional)
    [*] Life Insurance and annuity Contracts (Optional)
    [*] Reliability of Systems with Multiple Components or Processes (Optional)
    [*] Trigonometric Transformations (Optional)
    [*] Exercises
    [/LIST]
    [*] Sums and Products of Random Variables
    [LIST]
    [*] Techniques for Calculating the Distribution of a Sum
    [LIST]
    [*] Using the Joint Density
    [*] Using the Law of Total Probability
    [*] Convolutions
    [/LIST]
    [*] Distributions of Products and Quotients
    [*] Expectations of Sums and Products
    [LIST]
    [*] Formulas for the Expectation of a Sum or Product
    [*] The Cauchy-Schwarz Inequality
    [*] Covariance and Correlation
    [/LIST]
    [*] The Law of Large Numbers
    [LIST]
    [*] Motivating Example: Premium Determination in Insurance
    [*] Statement and Proof of the Law
    [*] Some Misconceptions Surround the Law of Large Numbers
    [/LIST]
    [*] The Central Limit Theorem
    [*] Normal Power Approximations (Optional)
    [*] Exercises
    [/LIST]
    [*] Mixtures and Compound Distributions
    [LIST]
    [*] Definitions and Basic Properties
    [*] Some Important Examples of Mixtures Arising in Insurance
    [*] Mean and Variance of a Mixture
    [*] Moment Generating Function of a Mixture
    [*] Compound Distributions
    [LIST]
    [*] General Formulas
    [*] Special Compound Distributions
    [/LIST]
    [*] Exercises
    [/LIST]
    [*] The Markowitz Investment Portfolio Selection Model
    [LIST]
    [*] Portfolios of Two Securities
    [*] Portfolios of Two Risky Securities and a Risk-Free Asset
    [*] Portfolio Selection with Many Securities
    [*] The Capital Asset Pricing Model
    [*] Further Reading
    [*] Exercises
    [/LIST]
    [*] Appendixes
    [LIST]
    [*] The Gamma Function
    [*] The Incomplete Gamma Function
    [*] The Beta Function
    [*] The Incomplete Beta Function
    [*] The Standard Normal Distribution
    [*] Mathematica commands for Generating the Graphs of Special Distributions
    [*] Elementary Financial Mathematics
    [/LIST]
    [*] Answers to Selected Exercises
    [*] Index
    [/LIST]
     
     
    Last edited: May 6, 2017
  2. jcsd
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