Geodesic
How many samples does it take to see all the balls in an urn?
Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 58-63.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let an urn contain $N$ balls, numbered from 1 to $N$. A random number of balls are drawn without replacements from the urn, their numbers are noted and the balls are then returned to the urn. This is done repeatedly, the sample sizes being independent identically distributed. Let $v$ be the number of samples needed to see all the balls. A simple approximation for $Ev$ and the asymptotic distribution of $v$ as $N\to\infty$ are obtained. 
@article{MZM_1998_64_1_a6,
     author = {G. I. Ivchenko},
     title = {How many samples does it take to see all the balls in an urn?},
     journal = {Matemati\v{c}eskie zametki},
     pages = {58--63},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a6/}
}
TY  - JOUR
AU  - G. I. Ivchenko
TI  - How many samples does it take to see all the balls in an urn?
JO  - Matematičeskie zametki
PY  - 1998
SP  - 58
EP  - 63
VL  - 64
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a6/
LA  - ru
ID  - MZM_1998_64_1_a6
ER  - 
%0 Journal Article
%A G. I. Ivchenko
%T How many samples does it take to see all the balls in an urn?
%J Matematičeskie zametki
%D 1998
%P 58-63
%V 64
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a6/
%G ru
%F MZM_1998_64_1_a6
G. I. Ivchenko. How many samples does it take to see all the balls in an urn?. Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 58-63. http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a6/

[1] Markoff A. A., Wahrscheinlichkeitsrechnung, Leipzig–Berlin, 1912

[2] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, M., 1976 | Zbl

[3] Kovalenko I. N., Levitskaya A. A., Savchuk M. N., Izbrannye zadachi veroyatnostnoi kombinatoriki, Naukova dumka, Kiev, 1986 | Zbl

[4] Ivanov V. A., Ivchenko G. I., Medvedev Yu. I., “Diskretnye zadachi v teorii veroyatnostei”, Itogi nauki i tekhn. Teoriya veroyatn. Matem. statistika. Teoretich. kibernetika, 22, VINITI, M., 1984, 3–60

[5] Polya G., “Eine Wahrscheinlichkeitsaufgabe in der Kundenwerbung”, Z. Angew. Math. Mech., 10:1–3 (1930), 96–97 | DOI

[6] Bekessy A., “A lottojatekal kapesolatos nehany cellabetoltesi problemazol, II”, Mat. Lapok, 16 (1965), 57–67 | MR

[7] Ivchenko G. I., Medvedev Yu. I., “Asimptoticheskoe povedenie chisla komplektov chastits v klassicheskoi zadache o razmeschenii”, Teoriya veroyatn. i ee primen., 11:4 (1966), 701–708 | MR | Zbl

[8] Ivchenko G. I., “Nekotorye predelnye teoremy v skheme razmescheniya”, Nekotorye prikladnye voprosy teorii veroyatn. i matem. statistika, Tr. MIEM, no. 32, MIEM, M., 1973, 111–119

[9] Sellke T. M., “How many samples does it take to see all the balls in a box?”, Ann. Appl. Probab., 5:1 (1995), 294–309 | DOI | MR | Zbl

[10] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, 2-e izd., Mir, M., 1964