Probability distributions in an ordered set of extracted elements

In summary, the conversation discussed the probability of finding a specific element in a specific position within an ordered set of randomly extracted elements from a set with a total order relation. The probability distribution function for this scenario was also mentioned, and it was mentioned that the problem has not been solved in literature. The suggestion was given to try solving it using the Mathematics Stack Exchange platform.
  • #1
jazzy
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TL;DR Summary
Finding the probability distributions in an ordered set of random extracted elements
Hello, I tried looking for an existing solution for the following problem:
"Assume that S is a set of d elements, and R is a total order relation on S. Assume that n elements are randomly extracted from S, and then they are ordered according to R. Which is the probability that in the i-th position of the ordered set of n elements there is the x-th element of S? (where the x-th element of S is intended according to the R).

In other words, which is the probability distribution function for the i-th position of the ordered set of n elements? Do you know whether such problem has already been solved? I did not find any specific solution in literature or elsewhere. I tried do find my own solution, but I would like to know if something already exist.
 
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  • #3
I don't think this is that hard. To get the xth element of R in the ith position, you need to pick x-1 elements smaller than it, and n-x-1 elements larger than it. You can just count the number of ways to do this. Why don't you give it a shot?
 
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Related to Probability distributions in an ordered set of extracted elements

1. What is a probability distribution in an ordered set of extracted elements?

A probability distribution in an ordered set of extracted elements is a mathematical function that describes the likelihood of each possible outcome occurring. It shows the relative frequency of each element being extracted from the set.

2. How is a probability distribution calculated?

A probability distribution is calculated by dividing the number of times an element appears in the set by the total number of elements in the set. This gives the probability of each element being extracted.

3. What is the difference between a discrete and continuous probability distribution?

A discrete probability distribution is used when the possible outcomes are countable, such as the number of heads when flipping a coin. A continuous probability distribution is used when the possible outcomes are uncountable, such as the height of a person.

4. How can probability distributions be represented graphically?

Probability distributions can be represented graphically using a histogram or a probability density function (PDF) plot. These graphs show the probability of each element being extracted and can help visualize the distribution.

5. What real-world applications use probability distributions in an ordered set of extracted elements?

Probability distributions in an ordered set of extracted elements are commonly used in fields such as statistics, finance, and engineering. They can be used to model and predict outcomes in various scenarios, such as stock market fluctuations or product demand.

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