It is important, of course, to provide real world contexts for mathematics whenever possible. Burkard has just stumbled upon a notable example, in a very old reddit thread. This is how the example is introduced, as the topic of a 1971 SIAM paper (submitted in 1969), by Steven Lippman and Sheldon Ross:
Lippmann and Ross’s paper is titled, with no great surprise, The Streetwalker’s Dilemma: A Job Shop model. The example also appears in Ross’s book, above, first published in 1970 and reprinted by Dover in 1991. In the book version, Ross considers “a prostitute working in the city of San Francisco”, although he then softens it a little by suggesting another context:
(Those readers who do not like to think in the above terms may view this as a model for determining whether or not a factory should accept or reject potential jobs, when the factory is only able to handle one job at a time.)
It’s an interesting problem, and teacher-readers should feel free to adapt it for a SAC. It’s just a shame that the problem is unsuitable for AMT. Unfortunately, the pronouns are all wrong.
Moving from streetwalkers to jobs in a factory is most unfortunate (and no, I won’t explain further).
But I’m sure AMT would be more than happy with a gender neutral streetwalker.
Unfortunately, the theory of distribution functions is not in the Study Design (the space is taken up by hypothesis testing in Specialist, confidence intervals etc). Although a well-written SAC could probably introduce the theory as well as other mathematical things that don’t appear in the study design.
“open-ended” was my first thought, but that would lead to a few to many MA15+ level comments, so I will leave it to the imagination of others to ponder further if they so choose.
Personally I think the concept of a merchant banker (not cockney slang) deciding which loans to underwrite might be closer to the original setting than a factory.
A banker can say “See me tomorrow”. This is not an option in other professions.
So can an optometrist, but for different reasons.
Thanks for sharing such an intriguing model – I started to ponder how it works mathematically using the 3rd year random process stuff learnt long ago…
Here is another link to the paper if Marty doesn’t mind me posting it here:
Click to access AD0699891.pdf
That’s fine. It’s a link to the 1969 preprint, which frames the question slightly differently. (Not that it matters for my post.)
Ross has got some of the best books on stats and probability. Used to use his books a lot as an undergrad and later.