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 Nov 30 accepted Calculating mean of sequence given means of subsets Nov 30 comment Calculating mean of sequence given means of subsets Thanks. That basically answers my question. Still wondering what the best possible estimate for the true mean would be, given the means of the partition, but that wasn't my question. Nov 30 comment Calculating mean of sequence given means of subsets Seems so. Was hoping that maybe there would be some way to find it as a mean of weighted means of means or something similar. Or that maybe the true mean would be the expected value of some random process that uses the values of $(a_k)$. But I don't know. Nov 30 comment Calculating mean of sequence given means of subsets Well, that's true, I said that much in the final paragraph, but we do not know the values of $l_i$. Nov 30 comment Calculating mean of sequence given means of subsets It is just an example, poorly constructed, it seems. I just came up with some numbers and wanted to use the n, the number of numbers in the sequence, instead of any fixed number. Nov 30 revised Calculating mean of sequence given means of subsets added tags Nov 30 asked Calculating mean of sequence given means of subsets Nov 17 awarded Yearling Nov 8 awarded Popular Question Oct 8 awarded Notable Question Jul 12 comment Probability that team $A$ has more points than team $B$ Surely you want to calculate P(A wins more games than B), which is clearly same as 1-P(B wins as many or fewer games than A). There are five games to be played. So... P(A wins more games than B) = P(A wins none and B wins none)+P(A wins one and B wins none) and so on. But there is probably some fancy way to calculate it that doesn't involve adding all the possibilities. Jun 19 accepted Estimating total number of twin primes Jun 14 comment Looking for group of polynomials with only real roots I changed the question to a hopefully more constructive one Jun 14 revised Looking for group of polynomials with only real roots Changed the nonquestion to a, hopefully, real question Jun 14 revised Looking for group of polynomials with only real roots Added some notes after comments Jun 14 comment Looking for group of polynomials with only real roots @JimBelk how about something that has something to do with the fact that the elements of the group are polynomials? If we look at the addition, we see the operation doesn't preserve the roots at all. On the other hand, multiplication preserves them completely. So, for a starting point, this mystery operation should keep the root structure somewhat intact; at least the roots of the result should depend on the roots of the components. Would also be nice if the group had some nontrivial subgroups, for example, polynomials with rational coefficients. Jun 14 asked Looking for group of polynomials with only real roots Jun 8 revised Factorization by multiplying and representation as difference of two squares Added what I had tried Jun 8 revised Factorization by multiplying and representation as difference of two squares Added more content Jun 5 asked Factorization by multiplying and representation as difference of two squares