What is the expected number of fixed points in permutations?

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SUMMARY

The expected number of fixed points in random permutations is definitively 1. This conclusion is based on the properties of permutations and the linearity of expectation in probability theory. The discussion highlights that while the intuitive answer is 1, formal proof may require deeper exploration of combinatorial principles.

PREREQUISITES
  • Understanding of permutations and combinatorial mathematics
  • Familiarity with probability theory, specifically the concept of expected value
  • Knowledge of linearity of expectation in statistics
  • Basic skills in mathematical proof techniques
NEXT STEPS
  • Study the concept of expected value in probability theory
  • Explore combinatorial proofs related to permutations
  • Learn about the linearity of expectation and its applications
  • Investigate advanced topics in combinatorial mathematics
USEFUL FOR

Mathematicians, statisticians, and students studying probability and combinatorics will benefit from this discussion, particularly those interested in the properties of permutations.

Dragonfall
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What is the expected number of fixed points in permutations? I got 1 as answer.
 
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I don't see any immediate way to prove it but that's what it looks like to me.
 

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