A probability problem: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
Line 7: | Line 7: | ||
You might be interested in trying to solve this problem. You can check your answer [http://www.dartmouth.edu/~chance/forwiki/ropes.pdf here]. | You might be interested in trying to solve this problem. You can check your answer [http://www.dartmouth.edu/~chance/forwiki/ropes.pdf here]. | ||
DISCUSSION QUESTION: | |||
Can you determine the distribution of the number of loops? If not estimate this by simulation. |
Revision as of 18:05, 16 July 2005
A Dartmouth student asked his math teacher Dana Williams if he could solve the following problem:
QUESTION: We start with n ropes and gather their 2n ends together.
Then we randomly pair the ends and make n joins. Let E(n)
be the expected number of loops. What is E(n)?
You might be interested in trying to solve this problem. You can check your answer here.
DISCUSSION QUESTION:
Can you determine the distribution of the number of loops? If not estimate this by simulation.