Topics

• Introductory Examples
        Tools:
            Interactive Model of Coin Flips
            Interactive Model of Die Rolls
            Interactive Model of Waiting Times
• Axioms of Probability and Immediate Consequences
        Task:   Compute Probabilities of Simple Events
• Counting and More Examples
  
        Task:   Several Counting Problems
• Some Basic Set Theory
        Tool:
            Examine Venn Diagrams
  
        Task:   Using Venn Diagrams
• Conditional Probability, Bayes’ Theorem, and Independence
  
        Task:   Determine Conditional Probabilities
  
        Task:   Use Bayes’ Theorem
• Random Variables
  
        Task:   Identify Random Variables
• Expected Value and Basic Properties
  
        Task:   Compute Expected Values
• Moments and the Moment Generating Function
  
        Task:   Compute Moments

• Chebyshevs’ Theorem
        Task:   Using Chebyshev’s Inequality
• Basic Models: Discrete Random Variables
          Uniform
          Bernoulli
          Binomial
          Geometric and Inverse Binomial
          Poisson
        Task:   Explore Binomial Densities
        Task:   Explore Geometric Densities
        Task:   Explore Poisson Densities
• Basic Models: Continuous Random Variables
          Uniform
          Exponential
          Normal
        Tools:
            Exponential Random Variables via Spreadsheets
            Standard Normal Random Variables via Spreadsheets
            General Normal Random Variables via Spreadsheets
            Visualize   $\chi^2$   Random Variables
            Visualize Student’s   $t$   Random Variables
        Task:   Explore Rectangular Densities
        Task:   Explore Exponential Densities
        Task:   Explore Normal Densities