Buffon's problem with a pivot needle

In this paper, we solve Buffon's needle problem for a needle consisting of two line segments connected in a pivot point.Comment: 4 pages, 1 figur

Thou shalt not say "at random" in vain: Bertrand's paradox exposed

We review the well known Bertrand paradoxes, and we first maintain that they do not point to any probabilistic inconsistency, but rather to the risks incurred with a careless use of the locution "at random". We claim then that these paradoxes spring up also in the discussion of the celebrated Buffon's needle problem, and that they are essentially related to the definition of (geometrical) probabilities on "uncountably" infinite sets. A few empirical remarks are finally added to underline the difference between "passive" and "active" randomness, and the prospects of any experimental decisionComment: 17 pages, 4 figures. Added: Appendix A; References 7, 8, 10; Modified: Abstract; Section 4; a few sentences elsewher

A probabilistic analysis of electrical equipment vulnerability to carbon fibers

The statistical problems of airborne carbon fibers falling onto electrical circuits were idealized and analyzed. The probability of making contact between randomly oriented finite length fibers and sets of parallel conductors with various spacings and lengths was developed theoretically. The probability of multiple fibers joining to bridge a single gap between conductors, or forming continuous networks is included. From these theoretical considerations, practical statistical analyses to assess the likelihood of causing electrical malfunctions was produced. The statistics obtained were confirmed by comparison with results of controlled experiments

Von Neumann and Computers

The title of this paper should not be Von Neumann and computers, but Von Neumann and the Von Neumann machine. Von Neumann may be famous for many things but humility was not one of them. Yet no one had anything bad to say about \u27good time\u27 Johnny Von Neumann; he just was too likeable. He gave massive parties and loved women, fast cars, jokes, noise, Mexican food, fine wine, and, most of all, mathematics. \u27Unbelievable\u27, said one of Von Neumann\u27s old friends, \u27He knew how to have a good time. His parties were once if not twice a week at 26 Wetcott Road. Waiters came around with drinks all night long. Dancing and loud laughter. With Von Neumann at the centre of it all he was a fantastically witty man.\u2

The illustration of the law of large numbers by simulations

Stochastická konvergence, zákon velkých čísel a centrální limitní věta představují důležitou část teorie pravděpodobnosti, která se často užívá v matematické statistice. Cílem této práce je popsat tuto teorii a demonstrovat ji na příkladech a grafických simulacích. Kromě simulací stochastické konvergence, zákona velkých čísel a centrální limitní věty pro některá diskrétní a spojitá rozdělení pravděpodobnosti práce obsahuje i několik zajímavých simulací a to simulaci Galtonovy desky, Buffonovy úlohy a Bertrandova paradoxu. K vytvoření grafických simulací byl použit programovací jazyk matlab.Stochastic convergence, law of large numbers and central limit theorem is an important part of probability theory, which is often used in mathematical statistics. The aim of this work is to describe this theory and demonstrate it with examples and graphical simulation. In addition simulation of stochastic convergence, law of large numbers and central limit theorem for some discrete and continuous probability distribution the work contains several interesting simulations for example simulation of Galton's box, Buffon's needle problem and Bertrand's paradox. To create a graphic simulation were used programming language matlab.

Probability and Statistics in Aerospace Engineering

This monograph was prepared to give the practicing engineer a clear understanding of probability and statistics with special consideration to problems frequently encountered in aerospace engineering. It is conceived to be both a desktop reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject