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Banach's match problem is a classic problem in probability attributed to Stefan Banach.Feller [1] says that the problem was inspired by a humorous reference to Banach's smoking habit in a speech honouring him by Hugo Steinhaus, but that it was not Banach who set the problem or provided an answer.
In probability theory, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: [1] Suppose we have a floor made of parallel strips of wood , each the same width, and we drop a needle onto the floor.
The matching is stable if there are no two elements which are not roommates and which both prefer each other to their roommate under the matching. This is distinct from the stable-marriage problem in that the stable-roommates problem allows matches between any two elements, not just between classes of "men" and "women". It is commonly stated as:
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975.
The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, [1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox. [2]