Expected value of integral = integral of expected value? Need help in the stats forum

In summary, the expected value of an integral is equal to the integral of the expected value. This concept is often used in statistics and probability to calculate the average or expected outcome of a continuous random variable. It involves finding the area under a curve and multiplying it by the probability of that outcome occurring. This relationship between the expected value and integral is important in various statistical calculations, and if you need help understanding it, you can seek assistance in the stats forum.
  • #1
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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  • #2


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

What is the expected value of an integral?

The expected value of an integral is the average value that would be obtained if the integral was computed over and over again. In other words, it is the mean value of the integral.

What is the integral of an expected value?

The integral of an expected value is the value that would be obtained if the expected value was integrated over the entire range of the variable. In other words, it is the area under the curve of the expected value function.

Why is the expected value of an integral equal to the integral of the expected value?

This is a fundamental property of expected values and integrals. It is based on the fact that the expected value and integral operators are both linear operators, meaning they can be moved in and out of each other without affecting the result.

What is the significance of the equality between expected value of integral and integral of expected value?

This equality is important because it allows us to calculate expected values and integrals interchangeably. It also allows us to use expected values to simplify complex integrals.

How is the concept of expected value of an integral used in statistics?

The concept of expected value of an integral is used in probability theory and statistics to calculate the average value of a random variable over a given range. This is useful for making predictions and estimating the likelihood of certain events occurring.

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