Expected Value for Intersection of Subset Sets in a Set?

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SUMMARY

The discussion centers on calculating the expected value for the intersection of two subsets, A and B, from a set X with n elements. The approach involves determining the probability of various intersection sizes and multiplying these probabilities by n. For n=3, there are 64 possible selections of the intersection, leading to complexities in defining the expected value when outcomes are non-numeric. Participants seek a more efficient method to tackle this general problem.

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  • Understanding of set theory and subsets
  • Familiarity with probability concepts
  • Basic knowledge of expected value calculations
  • Experience with combinatorial analysis
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  • Research combinatorial probability techniques
  • Learn about expected value in non-numeric contexts
  • Explore advanced set theory concepts
  • Investigate algorithms for efficient intersection calculations
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Mathematicians, data scientists, and statisticians interested in probability theory and set operations.

sylar
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Let X be a set with n elements, and let A,B be subsets of X. What is the general expected value for the intersection of these two sets?

Here for each n, we must find the possibility of having an intersection set of elements, multiply this probability by n, and then sum up the products we obtained.

Take the case when n=3. Then there are 8 different possibilities for choosing A, and also for B. Thus, there are 64 different possible selections of A int. B. We must find the possibility of having the set A int. B with n elements, where n=0,1,2,3, and this seems very complicated. So, is there a better approach for this (general) problem? Thanks!
 
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"Expected value" is normally a number. It is not at all clear to me how you would define the "expected value" when the outcomes are not themselves numeric.
 

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