Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.
As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
Read more about Probability Theory: History, Treatment, Probability Distributions, Convergence of Random Variables, Law of Large Numbers, Central Limit Theorem
Famous quotes containing the words probability and/or theory:
“Crushed to earth and rising again is an author’s gymnastic. Once he fails to struggle to his feet and grab his pen, he will contemplate a fact he should never permit himself to face: that in all probability books have been written, are being written, will be written, better than anything he has done, is doing, or will do.”
—Fannie Hurst (1889–1968)
“We commonly say that the rich man can speak the truth, can afford honesty, can afford independence of opinion and action;—and that is the theory of nobility. But it is the rich man in a true sense, that is to say, not the man of large income and large expenditure, but solely the man whose outlay is less than his income and is steadily kept so.”
—Ralph Waldo Emerson (1803–1882)