Show
Recommended textbook solutions
Probability and Statistics for Engineers and Scientists9th EditionKeying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers 1,204 solutions
Probability and Statistics for Engineering and the Sciences9th EditionJay L. Devore 1,589 solutions
Introduction to Probability1st EditionJessica Hwang, Joseph K. Blitzstein 601 solutions
Probability and Statistics for Engineering and the Sciences7th EditionJay L. Devore, R.C. Hibbeler 1,222 solutions Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics. There are several competing interpretations of the actual "meaning" of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure that endeavors to estimate parameters of an underlying distribution based on the observed distribution. A properly normalized function that assigns a probability "density" to each possible outcome within some interval is called a probability density function (or probability distribution function), and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a distribution function (or cumulative distribution function). A variate is defined as the set of all random variables that obey a given probabilistic law. It is common practice to denote a variate with a capital letter (most commonly ). The set of all values that can take is then called the range, denoted (Evans et al. 2000, p. 5). Specific elements in the range of are called quantiles and denoted , and the probability that a variate assumes the element is denoted .Probabilities are defined to obey certain assumptions, called the probability axioms. Let a sample space contain the union () of all possible events , so
and let and denote subsets of . Further, let be the complement of , so that
Then the set can be written as
where denotes the intersection. Then where is the empty set. Let denote the conditional probability of given that has already occurred, then The relationship
holds if and are independent events. A very important result states that
which can be generalized to
See alsoBayes' Theorem, Conditional Probability, Countable Additivity Probability Axiom, Distribution Function, Independent Statistics, Likelihood, Probability Axioms, Probability Density Function, Probability Inequality, Statistical Distribution, Statistics, Uniform Distribution Explore this topic in the MathWorld classroom Explore with Wolfram|AlphaReferencesEvans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, 2000.Everitt, B. Chance Rules: An Informal Guide to Probability, Risk, and Statistics. Copernicus, 1999.Goldberg, S. Probability: An Introduction. New York: Dover, 1986.Keynes, J. M. A Treatise on Probability. London: Macmillan, 1921.Mises, R. von Mathematical Theory of Probability and Statistics. New York: Academic Press, 1964.Mises, R. von Probability, Statistics, and Truth, 2nd rev. English ed. New York: Dover, 1981.Mosteller, F. Fifty Challenging Problems in Probability with Solutions. New York: Dover, 1987.Mosteller, F.; Rourke, R. E. K.; and Thomas, G. B. Probability: A First Course, 2nd ed. Reading, MA: Addison-Wesley, 1970.Nahin, P. J. Duelling Idiots and Other Probability Puzzlers. Princeton, NJ: Princeton University Press, 2000.Neyman, J. First Course in Probability and Statistics. New York: Holt, 1950.Rényi, A. Foundations of Probability. San Francisco, CA: Holden-Day, 1970.Ross, S. M. A First Course in Probability, 5th ed. Englewood Cliffs, NJ: Prentice-Hall, 1997.Ross, S. M. Introduction to Probability and Statistics for Engineers and Scientists. New York: Wiley, 1987.Ross, S. M. Applied Probability Models with Optimization Applications. New York: Dover, 1992.Ross, S. M. Introduction to Probability Models, 6th ed. New York: Academic Press, 1997.Székely, G. J. Paradoxes in Probability Theory and Mathematical Statistics, rev. ed. Dordrecht, Netherlands: Reidel, 1986.Todhunter, I. A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace. New York: Chelsea, 1949.Weaver, W. Lady Luck: The Theory of Probability. New York: Dover, 1963. Referenced on Wolfram|AlphaProbability Cite this as:Weisstein, Eric W. "Probability." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Probability.html Subject classificationsWhat branch of mathematics that deals with chance?probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
What refers to the branch of mathematics that deals with uncertainty?Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Mathematical measures of the likelihood of an event being true include probability theory, capacity, fuzzy logic, possibility, and credibility, as well as uncertainty.
What refers to the branch of mathematics that deals with uncertainty and its a measure or estimation of how likely it is that an event will occur?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
What is the branch of mathematics that deals with the collection organization presentation analysis interpretation of data?Statistics is the branch of mathematics that studies the collection, organization, analysis and interpretation of numerical data.
|