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 Jun 19 awarded Notable Question Sep 24 awarded Autobiographer Aug 6 awarded Popular Question Dec 19 revised Calculating coefficients of generating function added 106 characters in body Dec 19 comment Calculating coefficients of generating function But yes, conv is much closer to numeric calculation of the probabilities than resorting to numeric approximate calculations of derivatives of the generating function as suggested in the other answer. Dec 19 comment Calculating coefficients of generating function Thank you! This it closer to an answer I would like to accept. Still, I expect that there could be a way to completely get rid of generating function (as I understand it's designed just to simplify things for those who make by-hand calculations), as there might be other formulas using for example binomial coefficients (it's just a guess). Sep 29 revised Calculating coefficients of generating function added 1 characters in body Sep 29 asked Calculating coefficients of generating function Dec 19 awarded Self-Learner Nov 1 comment Is the rank of $AB$ always equal to the rank of $BA$? Thank you for the answer. I even started watching videos on the Khan Academy site about the nullspace of a matrix after reading you answer! After watching this video I'll recur to your answer and hope I'll managed to grasp it completely. Nov 1 awarded Scholar Nov 1 accepted Is the rank of $AB$ always equal to the rank of $BA$? Nov 1 comment Is the rank of $AB$ always equal to the rank of $BA$? @Phira My lack of ability to anderstand was primarily connected with the terms in English which I couldn't comprehend (English is not my native language): "full rank", "regard" in this meaning, finite sets; cardinality; dimensions. I may know these terms in my native language, but here in English they were beyond my ability to comprehend. Now with Gerry Myerson's explanation I seem to understand that the order of function application matters and the size of resultant range may differ. Nov 1 comment Is the rank of $AB$ always equal to the rank of $BA$? @GerryMyerson Thank you. I seem to understand now. Nov 1 awarded Teacher Nov 1 comment Is the rank of $AB$ always equal to the rank of $BA$? @Phira I can barely understand what you write. Oct 31 comment Is the rank of $AB$ always equal to the rank of $BA$? @AndréNicolas Thanks! I updated the answer. It worked. The only thing left that I can't understand is why the rank changes. Oct 31 awarded Editor Oct 31 revised Is the rank of $AB$ always equal to the rank of $BA$? added 62 characters in body Oct 31 comment Is the rank of $AB$ always equal to the rank of $BA$? @JasonDeVito Thanks for the hit. I made an answer basing on it. Still, I want some intuition why it's so. We can look on the first matrix in a multiplication as on some operator. And why if A operates on B the rank is r1 and when B operates on A is r2, and r1 is not equal to r2. The proof is a good thing, but it'll be forgotten over time. And only intuition is what will be carried over time.