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trondreitan (November 30, 1999 at 12:00 am)
Thanks. It's a bit frightening to have a reader of Cox in the audience. I bought the book, since Jaynes referred to it, but haven't read through it, yet. What you mention is a good illustration of expectancy, yes. There's also the thing about the minimizing quadratic error in an estimation problem, which yields expectancy. The difference between most likely and expectancy is something I'm planning on mentioning in the next clip.
clray123 (November 30, 1999 at 12:00 am)
I find the lottery metapher nice because it helps distinguish between "most likely" and "expected" - which are easily confused due to their intuitive similarity. A lottery can have a tiny "most likely" win (many worthless tickets), but still a pretty high expected value (a single ticket with a grand prize). With limited financial resources the "most likely" value seems to be more useful in spending decisions than the "expected" value.
clray123 (November 30, 1999 at 12:00 am)
Cox explains the meaning of "expected value" in "Algebra of Probable Inference" using a lottery example. There are winnable prizes of n different values in a lottery with m tickets. Each ticket may win one prize (or none). The "expected value" of the lottery is the break-even ticket price. Asking anything lower than that price makes the lottery organizer lose money after all tickets have been sold. Asking anything higher turns him a profit. |
