Determining if a list of numbers is a result of multiplication

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• alk10
In summary, the second collection of integers was generated by multiplying a random integer by a fraction in the range 0-2 and rounding to the nearest integer. This method is more likely to produce integers in the range 0-1000 than the first collection of integers, which consists of random integers with most (but not all) in the range 0-1000.
alk10
TL;DR Summary
Determining if a list of numbers is a result of multiplication
Suppose I have 2 collections of lists.

In the first collection the lists consists of random integers, with most (but not all) in the range 0-1000.
In the second collection the lists consist of integers calculated in the following way:
a. start with a random integer of similar range to the first list
b. multiply by some unknown fraction, typically (but not always) in the range 0-2.
c. round to the nearest integer

Given a particular list, I would like to be able to predict which collection it comes from.

I have tried taking the modulo from every number between 2-20 and looking at the remainder (as for example if the fraction in b) was exactly 2, then the elements mod 2 would always be zero), but couldn't find a noticeable difference. Would appreciate any ideas.

You have been very vague about the probabilities or distributions of the random behavior.
Phrases like "most (but not all)", "typically (but not always)", "random integers", etc. do not give us much to work with.
Since the second method might create a large number of integers that are beyond the range 0-1000, I would consider using that to make an educated guess about which method created the list. But your description is too vague to know if that is a feasible method.

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I would use a Bayesian approach for this (of course). "Simply" write down the data-generating models for your two possibilities and then do a Bayesian analysis for any parameters of the models. Then you can compare the models using Bayes factors or your favorite alternative Bayesian model comparison technique.

Just run a Monte Carlo on some randomly generated numbers to test

In general, the distributions of the two processes will be significantly different. You should be able to use a Chi-square goodness of fit test to determine which method is more likely for a given sample. Without more information about the distributions, I don't think that much more can be said.

1. How do you determine if a list of numbers is a result of multiplication?

To determine if a list of numbers is a result of multiplication, you can use the following steps:

1. Check if the list contains only numbers.
2. Find the product of the first two numbers in the list.
3. Compare the product to the third number in the list.
4. If the product is equal to the third number, continue this process for the rest of the numbers in the list.
5. If the product is not equal to any of the numbers in the list, then the list is not a result of multiplication.

2. Can a list of numbers be a result of multiplication if it contains negative numbers?

Yes, a list of numbers can be a result of multiplication even if it contains negative numbers. The same steps can be used to determine if the list is a result of multiplication, regardless of the presence of negative numbers.

3. What if the list contains decimals or fractions?

The same steps can be used to determine if a list of numbers is a result of multiplication, regardless of whether the numbers are decimals, fractions, or whole numbers. The only difference is that the product may also be a decimal or fraction.

4. Is there a faster way to determine if a list of numbers is a result of multiplication?

Yes, there are other methods such as using prime factorization or logarithms to quickly determine if a list of numbers is a result of multiplication. However, the steps mentioned earlier are the most straightforward and can be easily applied to any list of numbers.

5. What if the list contains repeating numbers?

If the list contains repeating numbers, the same steps can still be used to determine if it is a result of multiplication. However, it is important to note that the product may also be a repeating number. For example, a list of [2, 2, 4] is a result of multiplication (2 x 2 = 4), but the product is also a repeating number (2 x 2 = 4).

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