Probability: The Science of Uncertainty by Michael A. Bean

[P3X-018]

I'm looking for a good and pedagogic book about introductory Probability and statistics. I'm trying to get into this subject by self study. I only have knowledge in basic calculus, a little about multivariable calculus and linear algebra.
I studying physics but I don't how much I'll be needing to know about these theories, so something suitable for a physicist would be nice. It's also fine if it's 2 separate books one on probability and one on statistics.
These subjects explained in books like Riley's "Mathematical Methods for Physics and Engineering", are just not explained in enough details.

 

[Greg Bernhardt]

• Author: Michael A. Bean
• Title: Probability: The Science of Uncertainty
• Amazon Link: https://www.amazon.com/dp/0821847929/?tag=pfamazon01-20
• Prerequisities:

Table of Contents:

[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 Langauge 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]

 

[micromass]

• Author: Henk Tijms
• Title: Understanding Probability: Chance Rules in Everyday Life
• Amazon link https://www.amazon.com/dp/0521701724/?tag=pfamazon01-20
• Prerequisities: High School Algebra
• Level: Undergrad

Table of Contents:

[LIST]
[*] Preface
[*] Introduction
[*] Probability in Action
[LIST]
[*] Probability questions
[*] The law of large numbers and simulation
[LIST]
[*] The law of large numbers for probabilities
[*] Basic probability concepts
[*] Expected value and the law of large numbers
[*] The drunkard's walk
[*] The St. Petersburg paradox
[*] Roulette and the law of large numbers
[*] The Kelly betting system
[*] Random-number generator
[*] Simulating from probability distributions
[*] Problems
[/LIST]
[*] Probabilities in everyday life
[LIST]
[*] The birthday problem
[*] The coupon collector's problem
[*] Craps
[*] Gambling systems for roulette
[*] The 1970 draft lottery
[*] Bootstrap method
[*] Problems
[/LIST]
[*] Rare events and lotteries
[LIST]
[*] The binomial distribution
[*] The Poisson distribution
[*] The hypergeometric distribution
[*] Problems
[/LIST]
[*] Probability and Statistics
[LIST]
[*] The normal curve
[*] The concept of standard deviation
[*] The square-root law
[*] The central limit theorem
[*] Graphical illustration of the central limit theorem
[*] Statistical applications
[*] Confidence intervals for simulations
[*] The central limit theorem and random walks
[*] Falsified data and Benford's law
[*] The normal distribution strikes again
[*] Statistics and probability theory
[*] Problems
[/LIST]
[*] Chance trees and Bayes' rule
[LIST]
[*] The Monty Hall dilemma
[*] The test paradox
[*] Problems
[/LIST]
[/LIST]
[*] Essentials of Probability
[LIST]
[*] Foundations of probability theory
[LIST]
[*] Probabilistic foundations
[*] Compound chance experiments
[*] Some basic rules
[/LIST]
[*] Conditional probability and Bayes
[LIST]
[*] Conditional probability
[*] Bayes' rules in odds form
[*] Bayesian statistics
[/LIST]
[*] Basic rules for discrete random variables
[LIST]
[*] Random variables
[*] Expected value
[*] Expected value of sums of random variables
[*] Substitution rule and variance
[*] Independence of random variables
[*] Special discrete distributions
[/LIST]
[*] Continuous random variables
[LIST]
[*] Concept of probability density
[*] Important probability densities
[*] Transformation of random variables
[*] Failure rate functions
[/LIST]
[*] Jointly distributed random variables
[LIST]
[*] Joint probability densities
[*] Marginal probability densities
[*] Transformation of random variables
[*] Covariance and correlation coefficient
[/LIST]
[*] Multivariate normal distribution
[LIST]
[*] Bivariate normal distribution
[*] Multivariate normal distribution
[*] Multidimensional central limit theorem
[*] The chi-square test
[/LIST]
[*] Conditional distributions
[LIST]
[*] Conditional probability densities
[*] Law of conditional probabilities
[*] Law of conditional expectations
[/LIST]
[*] Generating functions
[LIST]
[*] Generating functions
[*] Moment-generating functions
[/LIST]
[*] Markov Chains
[LIST]
[*] Markov model
[*] Transient analysis of Markov chains
[*] Absorbing Markov chains
[*] Long-run analysis of Markov chains
[/LIST]
[/LIST]
[*] Appendix: Counting methods and [itex]e^x[/itex]
[*] Recommended reading
[*] Answers to odd-numbered problems
[*] Bibliography
[*] Index
[/LIST]