[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 383
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WWer, what does "first base size" mean ? The sum of the members ?
You need to determine (probabilistically (2sigma for example)) the size of the first base from the new base.
The size is, as I understand it, the range of extreme values, or what? In this case, if the distribution is known, the problem can be solved.
But if size is a number of numbers, I don't understand it. Give me an example, please.
Size is, I take it, the spread of the extremes, or what? In this case, with a known distribution, the problem can be solved.
But if size is a number of numbers, I don't understand something. Give me an example, please.
Let's take natural numbers for simplicity: 1 2 3 4 5 ... X. This is the "X" we need to find.
randomly choose a number from this base. e.g. "3"... the probability of choosing any number = 1/X.
Example. Suppose there are 10 numbers: 1 2 3 4 5 6 7 8 9 10 (I said 10 for the sake of example, actually this is the number we need to find)
Let's sample 20 numbers: 5 2 9 5 3 8 4 10 3 2 7 1 8 5 2 6 1 10 1
Here, now let's forget that we had the size of the first base, and only from the second base we need to find it.
It is clear that the first base will be much bigger and the numbers are not consecutive.
Wow, is this problem solvable at all?
Provided that the numbers in the first database have no repetitions, we can go through the subsequent samples and recalculate the number of elements (if the same number is repeated in them, then repetitions are not taken into account - just 1 time it was taken into account, and further occurrences are skipped). But where the guarantee that the original database does not contain more elements than we have been able to recalculate? Probability is probability. We would have to make a lot of samples. And the result will only be verified (no matter how many samples we made) - there will always be a probability that at least 1 element is not included into any sample....
Honestly, I don't get the idea. What if the numbers are the squares of natural numbers, i.e. 1, 4, 9, ..., 625? What is X equal to?
And how can it be estimated from a "sample" that is larger than the original population?
Can you hint at a practical application - what is it for?
Wow, is that problem solvable at all?
Provided that the first base numbers do not have repeats, you can go to subsequent selections and recalculate the number of elements (if one and the same number of repeated in them, then repetitions do not count - just 1 time it included, and further occurrences of missing). But where the guarantee that the original database does not contain more elements than we have been able to recalculate? Probability is probability. We would have to make a lot of samples. And the result will only be verified (no matter how many samples we made) - there will always be a probability that at least 1 element is not included into any sample....
Yes, of course it is)
so that's why i say "probabilistically".... so the answer should be something like this: base size 100000-110000 with 97% probability.... and if we do 300,000 samples we have a 95% probability of 90% of the base.
Honestly, I don't get the idea. What if the numbers are squares of natural numbers, i.e. 1, 4, 9, ..., 625? What is X equal to?
And how do I estimate it from a "sample" that is larger than the original population?
Can you give a hint of practical application - what's it for?
I send queries to the server, and in response I get 10 random user IDs from the database. Here I wanted to solve such a problem at the same time, that would know how many at least there ID, and how many queries to send)
zy. i have 400000 id now.
Hello, who can solve this problem?):
There is a base of different numbers. Randomly select numbers from it and formed another base (that is, there is already numbers can be repeated). You can select as many as you like, but it's a waste of resources and time.
You need to determine (probabilistically (2sigma for example)) the size of the first base from the new base.
+ It would also be nice to calculate how many samples should be made to get at least 90% of the first base.
MOJ of the sample multiplied by 2
determine the OLS from the sample and multiply by 2.
MOS of what?
you have selected 100 numbers from a base, if the base is numbered from 1 to .... X in order. then maybe *2 of these 100 numbers will be X
matad. rnd(2000) function gerends a random number from 1 to 2000. We took 100 values of i=0...100 and calculated everything with them. Of course, the result will not be exact, because this statistic is a confidence interval - you can also calculate it and, depending on accuracy you need, determine the right sample size