https://hal.inria.fr/hal-00980745Brennan, CharlotteCharlotteBrennanThe John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg] - WITS - University of the Witwatersrand [Johannesburg]Knopfmacher, ArnoldArnoldKnopfmacherThe John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg] - WITS - University of the Witwatersrand [Johannesburg]Descent variation of samples of geometric random variablesHAL CCSD2013[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-Méditerranée / I3s, Service Ist2014-04-18 16:43:252022-06-25 09:29:202014-04-18 17:09:14enJournal articleshttps://hal.inria.fr/hal-00980745/document10.46298/dmtcs.594application/pdf1In this paper, we consider random words ω1ω2ω3⋯ωn of length n, where the letters ωi ∈ℕ are independently generated with a geometric probability such that Pωi=k=pqk-1 where p+q=1 . We have a descent at position i whenever ωi+1 < ωi. The size of such a descent is ωi-ωi+1 and the descent variation is the sum of all the descent sizes for that word. We study various types of random words over the infinite alphabet ℕ, where the letters have geometric probabilities, and find the probability generating functions for descent variation of such words.