* 1982 – L. Neil Smith, The Probability Broach

* 2005 – L. Neil Smith ( writer ) and Scott Bieser ( illustrator ), The Probability Broach: The Graphic Novel

In L. Neil Smith's North American Confederacy series of novels, beginning with The Probability Broach, an alternate-history LaPorte is one of the major cities of North America, occupying roughly half the area of Larimer County, and with a population of over two million people ; whereas the city of Denver does not exist: In its place are the two small historic settlements of Saint Charles Town and Auraria.

In L. Neil Smith's alternate history novel The Probability Broach ( 1980 ), Albert Gallatin convinces the militia not to put down the rebellion, but instead to march on the nation's capital, execute George Washington for treason, and replace the Constitution with a revised Articles of Confederation.

He also wrote the novels Pallas, The Forge of the Elders, and The Probability Broach, each of which won the Libertarian Futurist Society's annual Prometheus Award for best libertarian science fiction novel.

* The Probability Broach ( 1980 ) is an alternate history novel in which history has taken a different turn because a single word in the Declaration of Independence was changed.

The Federalists are attempting to base a new civilization in interstellar space, kidnapping and enslaving a quarter of a million women as breeding stock from the anti-libertarian timeline from which the viewpoint character of The Probability Broach had escaped, with a plan to someday return in force to take over both of the alternate versions of Earth discovered by way of the P ' wheet / Thorens probability broach.

* In The Gallatin Divergence ( 1985 ), a time-traveling Federalist woman wants to change history but is opposed by the protagonists of The Probability Broach.

* The American Zone ( 2001 ), the most recent entry in the series, is a direct sequel to The Probability Broach concerned with the refugees from various anti-libertarian versions of the United States who take up residence in the Confederacy, and the response of the Confederacy to terrorist violence.

* The Probability Broach ( 1980, unexpurgated edition 1996, graphic novel 2004 )

* North American Confederacy, a fictional government in the novel The Probability Broach by L. Neil Smith

* L. Neil Smith's novel The Probability Broach has an alternate history of the United States, where None of the Above has received the most votes for President of the North American Confederacy on multiple occasions.

L. Neil Smith's series of novels starting with The Probability Broach take place in an alternate history where the United States becomes the " North American Confederacy ", which is basically anarcho-capitalist in nature, although there is the vestigial remnant of a government whose Continental Congress might meet every few decades.

In the series beginning with The Probability Broach he examines an alternate history world where the United States took a substantial turn away from centralized authority shortly after its founding.

* L. Neil Smith, The Probability Broach

Among the modern exponents of social science fiction in the Campbellian / Heinlein tradition is L. Neil Smith who wrote both The Probability Broach ( 1981 ) and Pallas, which dealt with alternative " sideways in time " futures and what a libertarian society would look like.

" Foresight: its Logical Laws, Its Subjective Sources ," ( translation of the 1937 article in French ) in H. E. Kyburg and H. E. Smokler ( eds ), Studies in Subjective Probability, New York: Wiley, 1964.

* Ramsey, Frank Plumpton ( 1931 ) " Truth and Probability " ( PDF ), Chapter VII in The Foundations of Mathematics and other Logical Essays, Reprinted 2001, Routledge.

The Science of Conjecture: Evidence and Probability Before Pascal ( Johns Hopkins ), ch.

** ( 1878 April ), " The Probability of Induction ", Popular Science Monthly, v. 12, pp. 705 – 718.

' Interpretations of Probability ', The Stanford Encyclopedia of Philosophy ( Summer 2003 Edition ), Edward N. Zalta ( ed.

Logical probabilities are conceived ( for example in Keynes ' Treatise on Probability ) to be objective, logical relations between propositions ( or sentences ), and hence not to depend in any way upon belief.

* Leon-Garcia, Albert ( 1994 ) Probability and Random Processes for Electrical Engineering ( 2nd edition ), Prentice Hall

In 1785, Condorcet wrote Essai sur l ’ application de l ’ analyse à la probabilité des décisions rendues à la pluralité des voix ( Essay on the Application of Analysis to the Probability of Majority Decisions ), one of his most important works.

( 1774 / 1986 ), " Memoir on the Probability of the Causes of Events ", Statistical Science 1 ( 3 ): 364 – 378.

* Stephen M. Stigler ( 1986 ), " Laplace's 1774 Memoir on Inverse Probability ", Statistical Science 1 ( 3 ): 359 – 363.

:-" Foresight: its Logical Laws, Its Subjective Sources ," ( translation of the 1937 article in French ) in H. E. Kyburg and H. E. Smokler ( eds ), Studies in Subjective Probability, New York: Wiley, 1964.

* J. Franklin, The Science of Conjecture: Evidence and Probability Before Pascal ( Baltimore: Johns Hopkins University Press, 2001 ), 192-3.

* J. Franklin, The Science of Conjecture: Evidence and Probability Before Pascal ( Johns Hopkins University Press, 2001 ), ch.

* R. L. E. Schwarzenberger ( 2000 ), The Language of Geometry, published in A Mathematical Spectrum Miscellany, Applied Probability Trust.

Guidance systems improve missile accuracy by improving its " Single Shot Kill Probability " ( SSKP ), which is part of combat survivability calculations associated with salvo combat model.

), Proceedings of the NATO Advanced Research Workshop on Modality, Probability and Bell's Theorems, Kluwer, 233-255.

* Unitary Group Representations in Physics, Probability, and Number Theory, 402 pages, Benjamin – Cummings Publishing Company ( 1978 ), ISBN 0-8053-6703-9

Feller remarks in his Introduction to the Theory of Probability & its Applications ( 3rd edition p. 450 ), " It is unfortunate that this remarkable paper passed practically unnoticed.

The most common reliability parameter is the mean time to failure ( MTTF ), which can also be specified as the failure rate ( this is expressed as a frequency or Conditional Probability Density Function ( PDF )) or the number of failures during a given period.

* Hájek, Alan, Interpretations of Probability, The Stanford Encyclopedia of Philosophy ( Summer 2003 Edition ), Edward N. Zalta ( ed.

Perhaps the first elaborate and systematic exposition was by John Venn, in The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability ( published editions in 1866, 1876, 1888 ).

Probability theory considers measures that assign to the whole set the size 1, and considers measurable subsets to be events whose probability is given by the measure.

Probability clouds are approximate, but better than the Bohr model, whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.

A distribution being " smoothed out " by summation, showing original Probability density function | density of distribution and three subsequent summations ; see Illustration of the central limit theorem for further details.

* Words of Estimative Probability, terms used by intelligence analysts to convey the likelihood of a future event occurring

His Tracts on the Probability of reaching the North Pole ( 1775 ) were written in consequence of the northern voyage of discovery undertaken by Captain Constantine John Phipps, afterwards Lord Mulgrave ( 1744 – 1792 ).

* Probability and Hume's Inductive Scepticism ( 1973 ) by David Stove

* Theory of Probability, ( translation by A Machi and AFM Smith of 1970 book ) 2 volumes, New York: Wiley, 1974-5.

Probability density function ( PDF ) methods for turbulence, first introduced by Lundgren, are based on tracking the one-point PDF of the velocity,, which gives the probability of the velocity at point being between and.

* Introduction to Probability and Statistics by William Mendenhall, Robert J. Beaver, Barbara M. Beaver, Thomson Brooks / Cole, 2005, page 159.

* An Intermediate Course in Probability, by Alan Gut, Springer, 1995, pages 5 – 6.

* Robert & Ellen Kaplan ( about 1930 / 40s -), authors of Nothing That Is, The Art of the Infinite: The Pleasures of Mathematics, and Chances Are: Adventures in Probability ( by Michael Kaplan and Ellen Kaplan ).

described machines that were governed by the Algorithmic Probability distribution.

* For a detailed description of Algorithmic Probability, see " Algorithmic Probability " by Hutter, Legg and Vitanyi in the scholarpedia.

It was introduced by Phillip M. Woodward in his 1952 paper " Information theory and inverse probability in telecommunication " in which he said the function " occurs so often in Fourier analysis and its applications that it does seem to merit some notation of its own " and his 1953 book " Probability and Information Theory, with Applications to Radar ".

* Probability, Random Variables, and Stochastic Processes by Papoulis, Athanasios 1965.

The influential textbook Probability Theory: The Logic of Science, written by the physicist and probability theorist E. T.

* Bachelier's theory of speculation is demonstrated by this 8 ft tall Probability Machine comparing stock market returns to the randomness of the beans dropping through the quincunx pattern.

Probability distributions are determined by assigning an expectation to each random variable.