A probability problem: Difference between revisions
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DISCUSSION QUESTION: | DISCUSSION QUESTION: | ||
(1) There is probably a history to this problem. If you know a source for this problem please mention this on the discussion page above. | |||
Can you determine the distribution of the number of loops? If not estimate this by simulation. | Can you determine the distribution of the number of loops? If not estimate this by simulation. |
Revision as of 18:10, 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:
(1) There is probably a history to this problem. If you know a source for this problem please mention this on the discussion page above.
Can you determine the distribution of the number of loops? If not estimate this by simulation.