Geodesic
On generating functions in solving probabilistic problems
Matematičeskoe obrazovanie, no. 3 (2024), pp. 10-16 
O. P. Vinogradov. On generating functions in solving probabilistic problems. Matematičeskoe obrazovanie, no. 3 (2024), pp. 10-16. http://geodesic.mathdoc.fr/item/MO_2024_3_a1/
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     author = {O. P. Vinogradov},
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     url = {http://geodesic.mathdoc.fr/item/MO_2024_3_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Using an example of two probabilistic problems, a method for finding generating functions will be shown. From the obtained explicit expressions for the generating functions, explicit expressions for the desired probabilities will be obtained. The first problem is related to Fibonacci numbers, and the second one is related to some combinatorial equalities.

[1] S. M. Voronin, A. G. Kulagin, “Metod proizvodyaschikh funktsii”, Kvant, 1984, no. 5, 11–18

[2] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, Mir, M., 1984, 289–290

[3] R. Grekhem, D. Knut, O. Patashnik, Konkretnaya matematika. Osnovanie informatiki, Mir, M., 1998, 329–331