On the Variance Associated to a Family of Ovaloids in the Euclidean Space E 3

Giuseppe Caristi; Giovanni Molica Bisci

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 1, page 87-98
  • ISSN: 0392-4041

Abstract

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In this paper we consider a random variable h arising from an intersection problem between a fixed convex body K 0 and a system of random independent and uniformly distributed ovaloids in E 3 .

How to cite

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Caristi, Giuseppe, and Molica Bisci, Giovanni. "On the Variance Associated to a Family of Ovaloids in the Euclidean Space $E_3$." Bollettino dell'Unione Matematica Italiana 10-B.1 (2007): 87-98. <http://eudml.org/doc/290366>.

@article{Caristi2007,
abstract = {In this paper we consider a random variable $h$ arising from an intersection problem between a fixed convex body $K_0$ and a system of random independent and uniformly distributed ovaloids in $E_3$.},
author = {Caristi, Giuseppe, Molica Bisci, Giovanni},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {87-98},
publisher = {Unione Matematica Italiana},
title = {On the Variance Associated to a Family of Ovaloids in the Euclidean Space $E_3$},
url = {http://eudml.org/doc/290366},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Caristi, Giuseppe
AU - Molica Bisci, Giovanni
TI - On the Variance Associated to a Family of Ovaloids in the Euclidean Space $E_3$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/2//
PB - Unione Matematica Italiana
VL - 10-B
IS - 1
SP - 87
EP - 98
AB - In this paper we consider a random variable $h$ arising from an intersection problem between a fixed convex body $K_0$ and a system of random independent and uniformly distributed ovaloids in $E_3$.
LA - eng
UR - http://eudml.org/doc/290366
ER -

References

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  1. BLASCHKE, W., Vorlesungen über Integralgeometrie, III Auflage, V.E.B. Deutscher Verlag der Wiss., Berlin (1955). MR76373
  2. CZUBER, E., Zur Theorie der geometrischen Wahrscheinlichketein, Sitz. Akad. Wiss. Wien, 90 (1884), 719-742. Zbl16.0180.01
  3. MOLICA BISCI, G., Random systems of planes in the Euclidean Space E 3 , Atti Acc. Scienze di Torino (2005). MR2256681
  4. POINCARÉ, H., Calcul des probabilitiés, ed. 2, Carré, Paris, 1912. Zbl43.0308.04
  5. SANTALÓ, L. A., Über das Kinematische Mass in Raum, Bull. Act. Sci. et Ind., n. 357, Hermann, Paris, (1936). 
  6. STOKA, M., La variance d'une variable aléatoire associée a une famille des ovales du plan euclidien, Bull. Ac. royale de Belgique (1973). MR322765
  7. STOKA, M., Sur les variances attachees aux quelques familles d'ovaloides dans l'espace E 3 , Pubb. Inst. Stat. Univ. Paris, 3-4 (1977), 99-105. MR488216

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