Student Puzzle Corner
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 =…
Here’s Anirban DasGupta’s latest puzzle. He says:
All of us were told as undergraduates, or perhaps Masters students, that an essential property of a point estimator is that it be consistent. And indeed, we usually or even always select estimators that are consistent. We are going to ask a provocative…