An Introduction to Geometrical Probability: Distributional Aspects with ApplicationsA useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research. |
Contents
PROPERTIES | 1 |
EXERCISES | 108 |
EXERCISES | 141 |
EXERCISES | 168 |
EXERCISES | 259 |
EXERCISES | 274 |
EXERCISES | 310 |
Random Parallelotope | 324 |
EXERCISES | 381 |
DISTRIBUTIONS OF RANDOM VOLUMES | 395 |
EXERCISES | 421 |
Appendix ASOME STATISTICAL CONCEPTS | 469 |
Appendix BSOME REVISION MATERIAL FROM | 477 |
Appendix CSOME RESULTS FROM SPHERICALLY | 483 |
BIBLIOGRAPHY | 491 |
AUTHOR INDEX | 539 |
Common terms and phrases
angle beta distributed Buchta Buffon's needle C₁ centre circle of radius closed convex curve Consider convex body convex figure convex hull coordinates cos² Crofton's denoted distance distributed random points distribution function equation Euclidean Euclidean space evaluated exact density Example expected number expected value fixed G-function gamma geometrical given h-th Hence hypergeometric function hypersphere independently and uniformly independently distributed integral integral geometry intersection invariant joint density Lemma line segment Mathai matrix mean value measure Mellin transform n-ball needle normalizing constant P₁ parallel lines parameters perimeter perpendicular plane Poisson arrivals probability problem r-content r₁ random chord random line random points inside random variables rectangle Section shown in Figure side surface area T₁ Theorem transformation type-1 beta u₁ uniformly distributed vector vertices volume content w₁ x-axis πη
Popular passages
Page 536 - DCC EXERCISES, including Hints for the Solution of all the Questions in "Choice and Chance.
Page 502 - DANIELS, HE, 1952. The covering circle of a sample from a circular normal distribution.