Probability: Decisions and Risk

• Adverse selection
• Airline overbooking
• The single-period inventory problem
• Simulating a normally-distributed random variable
• An R&D race
• Driving to the airport
• Contract bidding

In preparation for our course in March, please read through these ten pages of notes.

The (optional) material below comes from a five-week course on "probability" which I teach at Kellogg. Please feel free to use any of it for further review. In particular, since we'll be using simulation to analyze some problems during our class session, you might want to go through the workbook on "simulation" in the first section.

• 1: Introduction. The language of probability.
  Approaching complex problems via decomposition
  Probability diagrams
  Counting
  Preparing Excel for use at Kellogg
  Simulation
  KSim - A simulation tool
  Mini-Quiz #1
  Mini-Quiz answers
  

• 2: Probability and learning.
  Updating beliefs
  Notes on probability
  Computing probabilities
  Probability exercises
  Odds exercises
  Examples: Birthdays, bags of balls, "Let's Make a Deal!"
  Mini-Quiz #2
  Mini-Quiz answers
  

• 3: Random variables and expectations.
  Notes on random variables and expected value
  Exercises on expectations
  Example: Airline overbooking (the single-period inventory problem)
  The single-period inventory problem
  Comments on the role of spreadsheets in decision analysis
  Examples of optimization using Excel's "Solver" add-in
  Example: A 5-dice game (and optional material on matrix multiplication)
  Mini-Quiz #3
  Mini-Quiz answers
  

• 4: Random variables and variability.
  Notes on variability
  Variability calculations
  A graphical perspective on correlation
  Exercises on variability
  Example: Minimum-risk portfolios
  Mini-Quiz #4
  Mini-Quiz answers
  

• 5: Commonly-encountered probability distributions.
  Notes on the binomial, geometric, and normal distributions (exponential, Poisson, uniform, and beta distributions optional)
  Spreadsheet notes on the binomial and geometric distributions
  Exercises on the binomial and geometric distributions
  The Central Limit Theorem (demonstration spreadsheet)
  The cumulative normal distribution (demonstration spreadsheet)
  Exercises on the normal distribution
  Useful Excel probability functions
  Mini-Quiz #5
  Mini-Quiz answers
  

• 6: Decision trees.
  Notes on decision trees
  Connecticut Electronics
  Exercises on decision trees
  Mini-Quiz #6
  Mini-Quiz answers
  

• 7: Examples and applications.
  Monitoring a production process
  Sample exam: Miscellany
  Sample exam: Extreme Products Unlimited, Ltd.
  Sample exam: ATM operations
  

• 8: Simulation.
  Exercises on simulation