Is Expected Value of Integral Equal to Integral of Expected Value?

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SUMMARY

The discussion centers on the mathematical relationship between the expected value of an integral and the integral of an expected value, a topic that intertwines statistics and calculus. Participants express uncertainty regarding the validity of the statement made in a referenced book, indicating that the matter remains unresolved in the mathematical community. The original poster, clustro, seeks clarification and further insights from those with a stronger grasp of the concepts involved. The link to the discussion provides additional context and contributions from other users.

PREREQUISITES
  • Understanding of expected value in probability theory
  • Familiarity with integral calculus
  • Knowledge of statistical theory
  • Basic comprehension of mathematical proofs
NEXT STEPS
  • Research the properties of expected values in probability distributions
  • Study the Fundamental Theorem of Calculus
  • Explore the concept of Lebesgue integration
  • Investigate the implications of Fubini's Theorem in multivariable calculus
USEFUL FOR

Mathematicians, statisticians, students of calculus, and anyone interested in the intersection of statistics and calculus will benefit from this discussion.

clustro
Hello friends,

I am having some trouble with a particular statement an author made in a book.

Despite being a statistics question, it is at its heart, a calculus question. Perhaps someone here with a better understanding of the subject can help, because I'm not convinced the matter has been settled.

The link is here:

https://www.physicsforums.com/showthread.php?t=409853

I hope this isn't considered spam - it can be hard to categorize one's question.

All the best,

-clustro
 
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I added a comment to the other thread. I hope it helps.
 

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