Probability Theory Assignment—Discussion of Journal Articles

For class Wednesday, you must read both “Let’s Make a Deal: The Player’s Dilemma” and the corresponding “Comment.” These are articles from The American Statistician, which is a peer-reviewed journal published by the American Statistical Association.

General Discussion Guidelines

When reading articles for class discussion, I expect you to dig in, take notes (which you can easily reference in class), ask questions, and think carefully about the information presented. It’s a good idea to read the article twice—once to get the big-picture idea(s) and another time to ensure you understand the details.

Here are some examples of things to think about when doing the reading:

• What big issues are raised?

• What is the practical importance of these issues? (Uh, this might not always hold with the probability articles—but it will when we read articles on statistics.)

• What questions do you have? (Note—you should think hard, on your own, about how to answer the questions you have. If you’re still left wondering, then your question is a good one to raise in class discussion.)

• What was something surprising or interesting that you learned?

• Can you think of additional applications of these concepts (beyond the examples mentioned)?

When you’re done with the article, besides being prepared to discuss specifics (as mentioned above), you should also be prepared to give a general summary of the article—how would you summarize the main point(s) in just a few sentences? Are you prepared to answer questions asked by other students or by me?

Specific Guidelines for this Particular Discussion

Syed, Kelsey, Marie, Bree, Raj, and Nick (i.e., those not chosen during the last presentation day) will lead the class discussion of these articles. That said, the entire class is expected to participate thoughtfully and appropriately (e.g., asking questions, answers questions).

The discussion will begin with the leaders each presenting a solution to the Let’s-Make-a-Deal problem. [Random assignment: F1 (Marie), F2 (Raj), F3 (Syed), F4 (Nick), F5 (Bree), and F6 (Kelsey).] Each brief presentation will include an explanation of the proposed solution and it’s “flaw(s).” During this time, other students can and should ask questions if the explanations aren’t clear.

Then the following questions should be addressed (and other issues can be addressed, too):

· Does everyone understand the general solution presented by the authors? If not, what is confusing?

· What were the main points of Seymann’s “Comment”?

· What lingering questions do you have about either the article or the comment? Also, did you find any part of the articles especially interesting?

· Lastly, the “prisoner’s dilemma” is mentioned in the second paragraph of the article. Note that the Prisoner’s Dilemma is actually the name of a famous game-theory problem (not related to the Let’s-Make-a-Deal problem). The “prisoner’s paradox” (presented in a textbook by Mosteller in 1965) is roughly the following:

Three prisoners, A, B, and C, apply for parole. The parole board decides to release two of the three; the prisoners know this, but they don’t know which two will be released. Prisoner A realizes it is unethical to ask the warden if he, A, is to be released, but thinks of asking for the name of one prisoner other than himself who is to be released. He thinks if the warden says “B will be released,” his own chances have now gone down from 2/3 to 1/2, because either (A and B) or (B and C) will be released. And so, A decides not to reduce his chances by asking.

            How exactly is the prisoner’s paradox related to the Let’s-Make-a-Deal Problem?