Deadline: July 1, 2023
Student Puzzle Editor Anirban DasGupta poses another two problems, and says, “Once again, we propose one problem on statistics and one on probability. I think you will find both problems to be new to you and interesting. If you are not able to answer either problem analytically, send us meaningful computational answers, and we will look at them too.” Student IMS members: send us your solution, to either or both, to bulletin@imstat.org (with subject “Student Puzzle Corner”).
Puzzle 45.1.
Suppose
Prove that
Puzzle 45.2.
This interesting question was first raised by Brad Efron. How far from a t-confidence interval is the true value of a population mean when the t-interval misses the true value?
Formally, assume below that we have i.i.d. normal variables with mean
Derive an asymptotic approximation for
Solution to Puzzle 44
Well done to Soham Bonnerjee (University of Chicago) who sent a correct solution to 44.2 below. Anirban DasGupta explains:
Puzzle 44.1
This is a special case of an extremely interesting problem known as Moser’s worm problem. In 1966, Leo Moser asked what is the minimal area of a geometric region that can enclose any closed curve of a given length
Puzzle 44.2
Actually, the answers to the parts of this problem have nothing to do with the sequence of observations being i.i.d. from a standard Cauchy. Let
Although we can solve this problem directly by using calculations for