An Introduction to Geometrical Probability: Distributional Aspects with Applications
A 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.
DISTRIBUTIONS OF RANDOM VOLUMES
Appendix ASOME STATISTICAL CONCEPTS
Appendix BSOME REVISION MATERIAL FROM
Appendix CSOME RESULTS FROM SPHERICALLY
Identically Distributed Random Points
angle beta distributed Buchta centre characteristic function circle of radius closed convex curve compute Consider convex body convex figure convex hull cos2 defined denoted distributed random points distribution function equation Euclidean space evaluated exact density Example expected number expected value fixed following result G-function gamma given h-th Hence hypergeometric function hypersphere i-th identically distributed independently and uniformly independently distributed integral integral geometry intersection interval Jacobian joint density Lemma line segment lines cutting Mathai matrix mean value Mellin transform n-ball needle normalizing constant obtained orthogonal parallel lines parameters perimeter perpendicular pieces plane Poisson arrivals polar coordinates problem r-content random chord random line random points inside random triangle random variables rectangle region respectively rotation secant Section shown in Figure side surface area type-1 beta uniformly distributed uniformly distributed random vector vertices volume content x-axis
Page 536 - DCC EXERCISES, including Hints for the Solution of all the Questions in "Choice and Chance.
Page 502 - On the proof of the law of errors of observations", Philosophical Transactions of the Royal Society of London 160, 175-187.