Probability for dummies

Probability for dummies

Deborah J. Rumsey, 1961-

Book - 2006

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Subjects
Probabilities.
Published
Hoboken, N.J. : Wiley 2006.
Language
English
Main Author
Deborah J. Rumsey, 1961- (-)
Physical Description
xx, 358 p. : ill. ; 24 cm
Bibliography
Includes index.
ISBN
9780471751410
  • Introduction
  • About This Book
  • Conventions Used in This Book
  • What You're Not to Read
  • Foolish Assumptions
  • How This Book Is Organized
  • Icons Used in This Book
  • Where to Go from Here
  • Part I. The Certainty of Uncertainty: Probability Basics
  • Chapter 1. The Probability in Everyday Life
  • Figuring Out what Probability Means
  • Understanding the concept of chance
  • Interpreting probabilities: Thinking large and long-term
  • Seeing probability in everyday life
  • Coming Up with Probabilities
  • Be subjective
  • Take a classical approach
  • Find relative frequencies
  • Use simulations
  • Probability Misconceptions to Avoid
  • Thinking in 50-50 terms when you have two outcomes
  • Thinking that patterns can't occur
  • Chapter 2. Coming to Terms with Probability
  • A Set Notation Overview
  • Noting outcomes: Sample spaces
  • Noting subsets of sample spaces: Events
  • Noting a void in the set: Empty sets
  • Putting sets together: Unions, intersections, and complements
  • Probabilities of Events Involving A and/or B
  • Probability notation
  • Marginal probabilities
  • Union probabilities
  • Intersection (joint) probabilities
  • Complement probabilities
  • Conditional probabilities
  • Understanding and Applying the Rules of Probability
  • The complement rule (for opposites, not for flattering a date)
  • The multiplication rule (for intersections, not for rabbits)
  • The addition rule (for unions of the nonmarital nature)
  • Recognizing Independence in Multiple Events
  • Checking independence for two events with the definition
  • Utilizing the multiplication rule for independent events
  • Including Mutually Exclusive Events
  • Recognizing mutually exclusive events
  • Simplifying the addition rule with mutually exclusive events
  • Distinguishing Independent and Mutually Exclusive Events
  • Comparing and contrasting independence and exclusivity
  • Checking for independence or exclusivity in a 52-card deck
  • Chapter 3. Picturing Probability: Venn Diagrams, Tree Diagrams, and Bayes' Theorem
  • Diagramming Probabilities with Venn Diagrams
  • Utilizing Venn diagrams to find probabilities beyond those given
  • Using Venn diagrams to organize and visualize relationships
  • Proving intermediate rules about sets, Using Venn diagrams
  • Exploring the limitations of Venn diagrams
  • Finding probabilities for complex problems with Venn diagrams
  • Mapping Out Probabilities with Tree Diagrams
  • Showing multi-stage outcomes with a tree diagram
  • Organizing conditional probabilities with a tree diagram
  • Reviewing the limitations of tree diagrams
  • Drawing a tree diagram to find probabilities for complex events
  • The Law of Total Probability and Bayes' Theorem
  • Finding a marginal probability using the Law of Total Probability
  • Finding the posterior probability with Bayes' Theorem
  • Part II. Counting on Probability and Betting to Win
  • Chapter 4. Setting the Contingency Table with Probabilities
  • Organizing a Contingency Table
  • Defining the sample space
  • Setting up the rows and columns
  • Inserting the data
  • Adding the row, column, and grand totals
  • Finding and Interpreting Probabilities within a Contingency Table
  • Figuring joint probabilities
  • Calculating marginal probabilities
  • Identifying conditional probabilities
  • Checking for Independence of Two Events
  • Chapter 5. Applying Counting Rules with Combinations and Permutations
  • Counting on Permutations
  • Unraveling a permutation
  • Permutation problems with added restrictions: Are we having fun yet?
  • Finding probabilities involving permutations
  • Counting Combinations
  • Solving combination problems
  • Combinations and Pascal's Triangle
  • Probability problems involving combinations
  • Studying more complex combinations through poker hands
  • Finding probabilities involving combinations
  • Chapter 6. Against All Odds: Probability in Gaming
  • Knowing Your Chances: Probability, Odds, and Expected Value
  • Playing the Lottery
  • Mulling the probability of winning the lottery
  • Figuring the odds
  • Finding the expected value of a lottery ticket
  • Hitting the Slot Machines
  • Understanding average payout
  • Unraveling slot machine myths
  • Implementing a simple strategy for slots
  • Spinning the Roulette Wheel
  • Covering roulette wheel basics
  • Making outside and inside bets
  • Developing a roulette strategy
  • Getting Your Chance to Yell "BINGO!"
  • Ways to win at BINGO
  • The probability of getting BINGO - more complicated than you may think
  • Knowing What You're Up Against: Gambler's Ruin
  • The Famous Birthday Problem
  • Part III. From A to Binomial: Basic Probability Models
  • Chapter 7. Probability Distribution Basics
  • The Probability Distribution of a Discrete Random Variable
  • Defining a random variable
  • Finding and using the probability distribution
  • Finding and Using the Cumulative Distribution Function (cdf)
  • Interpreting the cdf
  • Graphing the cdf
  • Finding probabilities with the cdf
  • Determining the pmf given the cdf
  • Expected Value, Variance, and Standard Deviation of a Discrete Random Variable
  • Finding the expected value of X
  • Calculating the variance of X
  • Finding the standard deviation of X
  • Outlining the Discrete Uniform Distribution
  • The pmf of the discrete uniform
  • The cdf of the discrete uniform
  • The expected value of the discrete uniform
  • The variance and standard deviation of the discrete uniform
  • Chapter 8. Juggling Success and Failure with the Binomial Distribution
  • Recognizing the Binomial Model
  • Checking the binomial conditions step by step
  • Spotting a variable that isn't binomial
  • Finding Probabilities for the Binomial
  • Finding binomial probabilities with the pmf
  • Finding binomial probabilities with the cdf
  • Formulating the Expected Value and Variance of the Binomial
  • The expected value of the binomial
  • The variance and standard deviation of the binomial
  • Chapter 9. The Normal (but Never Dull) Distribution
  • Charting the Basics of the Normal Distribution
  • The shape, center, and spread
  • The standard normal (Z) distribution
  • Finding and Using Probabilities for a Normal Distribution
  • Getting the picture
  • Translating a problem into probability notation
  • Using the Z-formula
  • Utilizing the Z table to find the probability
  • Handling Backwards Normal Problems
  • Setting up a backwards normal problem
  • Using the Z table backward
  • Returning to X units, using the Z-formula solved for X
  • Chapter 10. Approximating a Binomial with a Normal Distribution
  • Identifying When You Need to Approximate Binomials
  • Why the Normal Approximation Works when n Is Large Enough
  • Symmetric situations: When p is close to 0.50
  • Skewed situations: When p is close to zero or one
  • Understanding the Normal Approximation to the Binomial
  • Determining if n is large enough
  • Finding the mean and standard deviation to put in the Z-formula
  • Making the continuity correction
  • Approximating a Binomial Probability with the Normal: A Coin Example
  • Chapter 11. Sampling Distributions and the Central Limit Theorem
  • Surveying a Sampling Distribution
  • Setting up your sample statistic
  • Lining up possibilities with the sampling distribution
  • Saved by the Central Limit Theorem
  • Gaining Access to Your Statistics through the Central Limit Theorem (CLT)
  • The main result of the CLT
  • Why the CLT works
  • The Sampling Distribution of the Sample Total (t)
  • The CLT applied to the sample total
  • Finding probabilities for t with the CLT
  • The Sampling Distribution of the Sample Mean, X
  • The CLT applied to the sample mean
  • Finding probabilities for X with the CLT
  • The Sampling Distribution of the Sample Proportion, p
  • The CLT applied to the sample proportion
  • Finding probabilities for p with the CLT
  • Chapter 12. Investigating and Making Decisions with Probability
  • Confidence Intervals and Probability
  • Guesstimating a probability
  • Assessing the cost of probably (hopefully?) being right
  • Interpreting a confidence interval with probability
  • Probability and Hypothesis Testing
  • Testing a probability
  • Putting the p in probability with p-values
  • Accepting the probability of making the wrong decision
  • Putting the lid on data snoopers
  • Probability in Quality Control
  • Part IV. Taking It Up a Notch: Advanced Probability Models
  • Chapter 13. Working with the Poisson (a Nonpoisonous) Distribution
  • Counting On Arrivals with the Poisson Model
  • Meeting conditions for the Poisson model
  • Pitting Poisson versus binomial
  • Determining Probabilities for the Poisson
  • The pmf of the Poisson
  • The cdf of the Poisson
  • Identifying the Expected Value and Variance of the Poisson
  • Changing Units Over Time or Space: The Poisson Process
  • Approximating a Poisson with a Normal
  • Satisfying conditions for using the normal approximation
  • Completing steps to approximate the Poisson with a normal
  • Chapter 14. Covering All the Angles of the Geometric Distribution
  • Shaping Up the Geometric Distribution
  • Meeting the conditions for a geometric distribution
  • Choosing the geometric distribution over the binomial and Poisson
  • Finding Probabilities for the Geometric by Using the pmf
  • Building the pmf for the geometric
  • Applying geometric probabilities
  • Uncovering the Expected Value and Variance of the Geometric
  • The expected value of the geometric
  • The variance and standard deviation of the geometric
  • Chapter 15. Making a Positive out of the Negative Binomial Distribution
  • Recognizing the Negative Binomial Model
  • Checking off the conditions for a negative binomial model
  • Comparing and contrasting the negative binomial, geometric, and binomial models
  • Formulating Probabilities for the Negative Binomial
  • Developing the negative binomial probability formula
  • Applying the negative binomial pmf
  • Exploring the Expected Value and Variance of the Negative Binomial
  • The expected value of the negative binomial
  • The variance and standard deviation of the negative binomial
  • Applying the expected value and variance formulas
  • Chapter 16. Remaining Calm about the Hypergeometric Distribution
  • Zooming In on the Conditions for the Hypergeometric Model
  • Finding Probabilities for the Hypergeometric Model
  • Setting up the hypergeometric pmf
  • Breaking down the boundary conditions for X
  • Finding and using the pmf to calculate probabilities
  • Measuring the Expected Value and Variance of the Hypergeometric
  • The expected value of the hypergeometric
  • The variance and standard deviation of the hypergeometric
  • Part V. For the Hotshots: Continuous Probability Models
  • Chapter 17. Staying in Line with the Continuous Uniform Distribution
  • Understanding the Continuous Uniform Distribution
  • Determining the Density Function for the Continuous Uniform Distribution
  • Building the general form of f(x)
  • Finding f(x) given a and b
  • Finding the value of b given f(x)
  • Drawing Up Probabilities for the Continuous Uniform Distribution
  • Finding less-than probabilities
  • Finding greater-than probabilities
  • Finding probabilities between two values
  • Corralling Cumulative Probabilities, Using F(x)
  • Figuring the Expected Value and Variance of the Continuous Uniform
  • The expected value of the continuous uniform
  • The variance and standard deviation of the continuous uniform
  • Chapter 18. The Exponential (and Its Relationship to Poisson) Exposed
  • Identifying the Density Function for the Exponential
  • Determining Probabilities for the Exponential
  • Finding a less-than probability for an exponential
  • Finding a greater-than probability for an exponential
  • Finding a between-values probability for an exponential
  • Figuring Formulas for the Expected Value and Variance of the Exponential
  • The expected value of the exponential
  • The variance and standard deviation of the exponential
  • Relating the Poisson and Exponential Distributions
  • Part VI. The Part of Tens
  • Chapter 19. Ten Steps to a Better Probability Grade
  • Get Into the Problem
  • Understand the Question
  • Organize the Information
  • Write Down the Formulas You Need
  • Check the Conditions
  • Calculate with Confidence
  • Show Your Work
  • Check Your Answer
  • Interpret Your Results
  • Make a Review Sheet
  • Chapter 20. Top Ten (Plus One) Probability Mistakes
  • Forgetting a Probability Must Be Between Zero and One
  • Misinterpreting Small Probabilities
  • Using Probability for Short-Term Predictions
  • Thinking That 1-2-3-4-5-6 Can't Win
  • "Keep 'em Coming ... I'm on a Roll!"
  • Giving Every Situation a 50-50 Chance
  • Switching Conditional Probabilities Around
  • Applying the Wrong Probability Distribution
  • Leaving Probability Model Conditions Unchecked
  • Confusing Permutations and Combinations
  • Assuming Independence
  • Appendix. Tables for Your Reference
  • Binomial Table
  • Normal Table
  • Poisson Table
  • Index

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