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

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## For those who have used this book

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4. ### Strongly don't Recommend

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1. Jan 19, 2013

### Greg Bernhardt

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
[*] Exercises
[/LIST]
[*] A Survey of Some Basic Concepts Through Examples
[LIST]
[*] Payoff in a Simple Game
[*] Choosing Between Payoffs
[*] 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
[*] 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
[*] 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]
[*] Index
[/LIST]

Last edited: May 6, 2017