Student Puzzle Corner
We pose a classic problem, variously known as the taxicab problem or the German tank problem (named after its historical application, by Allied forces in World War II, to the estimation of the monthly rate of German tank production from very few data).
We have a finite population $\mathcal{X}$ with…
Contributing Editor Anirban DasGupta writes on the previous problem, which was about phase transitions:
If the common probability that each observer tells the truth on any given instance is $p$, and if there are $m$ such observers, and if there are $n$ options (colors) to choose from, then by…
The deadline for the student puzzle about phase transitions has been extended to December 1. If you’re a student member, email us your solution: bulletin@imstat.org…
In Anirban DasGupta’s latest puzzle, we’re looking at a delicate and fascinating phenomenon pervasive in mathematics and probability: phase transition. A system’s evolution is being driven or influenced by some underlying force or parameter, and when that parameter just crosses a suitable critical boundary or threshold, the system undergoes a…
Congratulations to the two student members who sent correct answers to this puzzle: Yudong Chen (University of Cambridge, UK) and Zhen Huang (Columbia University, USA). Here’s Anirban DasGupta’s solution:
Using the notation of the problem, the recorded values $Y_1, Y_2, \cdots $ are iid with
$E(Y_i) = \sum_{i =…