Expected Value for Intersection of Subset Sets in a Set?

In summary, the expected value for the intersection of two subsets A and B of a set X with n elements can be calculated by finding the probability of having an intersection set of elements for each n and multiplying it by n, then summing up the products. However, this approach may become complicated for larger values of n, and it is unclear if there is a better approach for this problem.
  • #1
sylar
11
0
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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  • #2
"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.
 

1. What is expected value for sets?

The expected value for sets is a mathematical concept that represents the average outcome of a random experiment or event. It is calculated by multiplying each possible outcome by its probability and summing them together.

2. How is expected value for sets used in scientific research?

Expected value for sets is commonly used in scientific research to analyze and predict outcomes of experiments or events. It allows scientists to make informed decisions based on the likelihood of different outcomes and their associated values.

3. Can expected value for sets be negative?

Yes, expected value for sets can be negative. This means that the average outcome of the experiment or event is less than zero, indicating a potential loss rather than a gain.

4. What is the difference between expected value for sets and actual value?

The expected value for sets represents the average outcome of a random experiment, while the actual value is the specific outcome that occurs in a given experiment. Expected value is a theoretical concept, while actual value is based on real-world data.

5. How can expected value for sets help in decision making?

Expected value for sets can help in decision making by providing a quantitative measure of the average outcome of an experiment or event. This allows for informed decision making based on the probabilities and values associated with different outcomes.

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