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Topic: Algebra of random variables

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  NationMaster - Encyclopedia: Algebra of random variables
In the algebraic axiomatization of probability theory, one of whose main proponents was Irving Segal, the primary concept is not that of probability of an event, but rather that of a random variable.
The measurable space and the probability measure arise from the random variables and expectations by means of well-known representation theorems of analysis.
An expectation E on an algebra A of random variables is a normalized, positive linear functional.
www.nationmaster.com /encyclopedia/Algebra-of-random-variables   (645 words)

 Registrar's Office | Fall 2006 Course Schedule | Applied Math
Topics include descriptive statistics, probability models, random variables, expectation, sampling, the central limit theorem, classical and robust estimation of location, confidence intervals, hypothesis testing, two-sample problems, introductory analysis of variance, and introductory nonparametric methods.
Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, goodness-of-fit.  Students cannot receive credit for both 550.310 and 550.311.
Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, and goodness-of-fit will be covered.
www.jhu.edu /registrar/sched_crfall06/appliedmath.html   (1841 words)

 Probability - Wikipedia, the free encyclopedia
There are others who argue that probability is properly applied only to random events as outcomes of some specified random experiment, for example sampling from a population; this is the frequentist interpretation.
There are several other interpretations which are variations on one or the other of those, or which have less acceptance at present.
He can't decide whether this is just a random event—after all, it is possible (although unlikely) that a fair coin would give this result—or whether his assumption that the coin is fair is at fault.
en.wikipedia.org /wiki/Probability   (2765 words)

 Random Variables and Expectation
If a random variable is uniformly distributed, that means that the probability of landing in a particular interval is equal to the size of that interval divided by the size of the entire distribution.
In general, the expected value of a random variable, written as E(X), is equal to the weighted average of the outcomes of the random variable, where the weights are based on the probabilities of those outcomes.
Random variable X has a mean of 8 and a standard deviation of 4.
arnoldkling.com /apstats/chapter7.html   (2328 words)

 [No title]
A random variable is not a variable in the same sense the word is used in calculus or algebra: It is something that takes a random value, depending on the outcome of a random experiment.
The number of random draws with replacement from a 0-1 box until the first time a ticket labeled "1" is drawn is a random variable with a geometric distribution with parameter p=G/N, where G is the number of tickets labeled "1" in the box and N is the total number of tickets in the box.
Even though the random variable X counts "successes" in a fixed number (four) of independent trials, it does not have a binomial probability distribution, because the probability of success is not the same in every trial: It is 1/2 in the trials that involve the coin, and 1/6 in the trials that involve the die.
www.stat.berkeley.edu /users/stark/SticiGui/Text/ch12.htm   (5742 words)

 math lessons - Probability theory   (Site not responding. Last check: 2007-10-10)
Two crucial concepts in the theory of probability are those of a random variable and of the probability distribution of a random variable; see those articles for more information.
A random variable is a measurable function on Ω.
Others assign probabilities to propositions that are uncertain according either to subjective degrees of belief in their truth, or to logically justifiable degrees of belief in their truth.
www.mathdaily.com /lessons/Probability_theory   (754 words)

 Discrete Random Variables
The random variable (r.v.) X is the event that we are considering.
Let X be the random variable representing the number of times we throw the die.
The cumulative distribution function (c.d.f.) of a discrete random variable X is the function F(t) which tells you the probability that X is less than or equal to t.
www.mathsrevision.net /alevel/statistics/discrete_random_variables.php   (639 words)

 3. Random Variables & Probability Distributions
A discrete random variable, x, occurs with probability f(x) and is an element of the finite or countably infinite set of all possible events X.
A continuous random variable is defined for some interval on the line of real numbers; but the probability that a continuous random variable, x, takes on any specified real value in the interval is equal to zero.
The normal, or Gaussian, distribution is widely applicable as a probability model for continuous random variables that may be thought of as resulting from the sum of a large number of small effects.
mcardle.oncology.wisc.edu /mstat/Mhelp/StatNotes-3.html   (4656 words)

 Lost causes in physics, by R. F. Streater   (Site not responding. Last check: 2007-10-10)
By allowing that the random variable chosen by A to model X if B measures Y to be a different random variable from the one she chooses if Bob measures Z, one can reproduce the quantum correlations exactly.
The representation of the observables as random variables is, in each case, then an immediate consequence of Gelfand's general construction of a representation of a commutative C* sub-algebra by bounded random variables defined on the spectrum of the subalgebra.
He relaxed the requirement that the quantum algebra be irreducible, and was able to find a class of homomorphic mappings from the Poisson algebra to the algebra of linear operators on the space of smooth functions on phase space.
www.mth.kcl.ac.uk /~streater/lostcauses.html   (12381 words)

 Course Listing For STAT   (Site not responding. Last check: 2007-10-10)
Types of sampling and types of statistical studies; basic, probability, random variables and their distribution, specific discrete and continuous distributions producing models using probability and simulation; summarizing and exploring data using graphical techniques and numerical summaries; exploring and making inferences for relationship between two variables: contingency tables, chi-sq.
Relevant matrix theory, multivariate random vectors, exact and asymptotic distributions, multivariate normal distribution (MVN), Q-Q plots, sampling from MVN and inference for population mean vector, covariance matrix, correlation matrix, MANOVA, principal component analysis, factor analysis, discriminant analysis and classification and clustering.
The relevant matrix theory, multivariate random vectors and their distributions, multivariate normal distribution (MVN), sampling from MVN and inference for population mean vector, covariance matrix, correlation matrix, multivariate ANOVA, principal component analysis, factor analysis, discriminant analysis and classification.
www.stat.uga.edu /courses/stat.html   (2070 words)

 Citations: Stochastic Analysis - Malliavin (ResearchIndex)
The material in this section represents a synthesis of these various frameworks emphasizing those aspect that are most directly related to the formulation of the stochastic finite element method.
P ; H;F H) In this notation, H specifies the Gaussian subspace of random variables with which events in the algebra FH are associated, while the algebra F H contains the events that are independent of H, and is referred to as the transverse oe algebra or the algebra of transverse events
The oe algebra, F, of all random variables is then given by the tensor product F = FH Omega F H ; 5) indicating that an arbitrary event could involve combinations of events associated with H and others that are not.
citeseer.ist.psu.edu /context/669318/0   (774 words)

 [No title]   (Site not responding. Last check: 2007-10-10)
Lecture 1: Probability distributions Lecture 2: Moments of distributions Lecture 3: CCD bias and flat-fielding Lecture 4: Multivariate distributions: Algebra of random variables, covariance, correlation Lecture 5: Functions of random variables; statistics; sample mean, variance; weighting Lecture 6: Variance and bias of transformed variables.
Scaling a profile to fit data using algebra of random variables.
Lecture 10: ML estimators and their variances; fitting a line to data; correlated versus orthogonal parameters.
star-www.st-and.ac.uk /~kdh1/ada/lectures/ADAindex   (198 words)

Conditional event algebra (CEA) was developed in order to represent conditional probabilities with differing antecedents by the probability evaluation of well-defined individual "conditional" events in a single larger space extending the original unconditional one.
A major application of CEA is to data fusion problems, especially the testing of hypotheses concerning the similarity or redundancy among inference rules through use of probabilistic distance functions which critically require probabilistic conjunctions of conditional events.
Relational event algebra (REA) is a further extension of CEA, whereby functions of probabilities formally representing single event probabilities - not just divisions as in the case of CEA - are shown to represent actual "relational" events relative to appropriately determined larger probability spaces.
quanterion.com /Documents/Documents.asp?ArgVal=336   (292 words)

 Means and variances of random variables   (Site not responding. Last check: 2007-10-10)
Example: Consider a random variable x that assumesthe values 1,2,3 with respective probabilities 60%, 30%, 10%.
To illustrate this, note that in the example above, onewould "expect" this distribution of the random variable in tentrials: {1,1,1,1,1,1,2,2,2,3}.
The mean,standard deviation, and variance for T are, respectively, 3,3.16227766, and 10 respectively.
www.herkimershideaway.org /apstatistics/ymmsum99/ymm772.htm   (559 words)

 Matrix Algebra for Markov Chains
Applied business computation lends itself well to calculations that use matrix algebra.
Matrix algebra refers to computations that involve vectors (rows or columns of numbers) and matrices (tables of numbers), as wells as scalars (single numbers).
In a great many cases, the simplest way to describe a set of relationships uses matrix algebra.
home.ubalt.edu /ntsbarsh/Business-stat/Matrix/Mat4.htm   (778 words)

 Probability, Random Variables and Random Signal Principles.
In a simple random sample the m consecutive units are drawn with equal probabilities from the units concerned.
The sample space and the algebra are the same as in the case of sampling without replacement, but the probability measure P is different.
algebra generated by the collection (23) of all open intervals in is called the Euclidean Borel field, denoted by B, and its members are called the Borel sets.
www.clickerado.com /l/lotto/random_variables.htm   (2047 words)

 Course Listing For STAT
Topics include: descriptive statistics, probability, random variables and distributions, sampling distributions of sample mean and proportion, statistical inference for population mean and proportion for single sample, comparison of two population means and proportions, simple linear regression, and introduction to multiple regression.
Univariate analysis for measurement data using graphs and numerical summaries; bivariate analysis for measurement data using scatterplots, correlation, and fitting lines; describing categorical data; sampling methods; observational and experimental studies; describing random behavior; binomial and normal distributions; sampling distributions; confidence intervals and significance testing; pedagogy methods for instruction and integrating technology.
Sampling and statistical studies; basic probability; random variables and their distributions; exploring data using graphical techniques and numerical summaries; exploring relationships between two variables: chi-sq.
bulletin.uga.edu /bulletin/courses/descript/STAT.html   (2631 words)

 Symbolic manipulation of random variables   (Site not responding. Last check: 2007-10-10)
This research considers a generalized version of the univariate change-of-variable technique for transforming random variables.
Specifically, the transformation can range from 1-to-1 to many-to-1 on various subsets of the support of the random variable of interest.
The research includes an implementation of the theorem in a symbolic algebra computer language that automates the technique.
www.math.wm.edu /~leemis/research2.html   (70 words)

 SYLLABUS_U01   (Site not responding. Last check: 2007-10-10)
Statistics at a level which assumes knowledge of high school algebra.
Descriptive statistics, random variables, probability distributions, sampling distributions, confidence interval estimation and hypothesis testing.
Probability distributions, random variables, discrete probability distribution table.
www.stat.uga.edu /courses/stat2000.html   (787 words)

 Free Online MIT Course Materials | Mathematics | MIT OpenCourseWare
Because the career objectives of undergraduate mathematics majors are so diverse, each undergraduate's program is individually arranged through collaboration between the student and his or her faculty advisor.
In general, students are encouraged to explore the various branches of mathematics, both pure and applied.
Various MIT faculty are openly sharing these resources as a service to MIT OCW users.
ocw.mit.edu /OcwWeb/Mathematics   (371 words)

 Exact Analysis of Postdetection Combining for DPSK and NFSK Systems Over Arbitrarily Correlated Nakagami Channels   (Site not responding. Last check: 2007-10-10)
The difficulty arises from inherent nonlinearity in noncoherent detection and from attempts to determine explicitly the probability density function of the total signal-to-noise ratio at the combiner output.
Curland, "Distribution of the maximum of the arithematic mean of correlated random variables," Ann.
Springer, The Algebra of Random Variables.New York: Wiley, 1979.
www.comsoc.org /comm/private/1998/nov/1459_46comm11-zhang.html   (418 words)

 Probability and Random Processes: With Applications to Signal Processing and Communications
It is aimed at graduate students as well as practicing engineers, and includes unique chapters on narrowband random processes and simulation techniques.
The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more.
Probability and Random Processes also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields.
www.scitechpub.com /Miller_Prob.htm   (217 words)

 Astronomical Data Analysis   (Site not responding. Last check: 2007-10-10)
ada04.ppt Multivariate distributions: Algebra of random variables, covariance, correlation
ada10.ppt ML estimators and their variances; fitting a line to data; correlated versus orthogonal parameters.
ada15.ppt Lecture 15: Error bar as unit of distance; fitting a line to 2 random variables; Gram-Schmidt orthogonalization.
star-www.st-and.ac.uk /~kdh1/ada/lectures/adalectures.html   (152 words)

 Introduction to Econometrics - Small and large sample properties of estimators
If Y is a random variable of independent observations with a probability distribution f then the joint distribution can be written as
The function of the unknown parameter, as a function of the values of the random variable, is called the
likelihood function which has the same structure as the joint probability function but is dependent on the random variable in stead of the unknown parameter.
www.xycoon.com /estimator_properties.htm   (768 words)

 Fields Institute - Lecture Audio and Slides
Dietmar Bisch, Vanderbilt University: Subfactors and Planar Algebras
Benoit Collins, Université Claude Bernard Lyon 1 and Ottawa: Weingarten calculus on enveloping algebras and non-commutative random matrices
Vaughan Jones, University of California, Berkeley: The graded algebras of a planar algebra
www.fields.utoronto.ca /audio   (2295 words)

 EECS 226A
Week three: Events and random variables; mutual exlusiveness and independence of events; difference between independence of events and independence of random variables (the local minimum problem in homework one); conditional probability (the filp-coin problem in homework one); review of linear algebra continued (if time allows).
Week four: Some examples in linear algebra; Gaussian random variables example: exercise 2.3 in the Gaussian notes.
Week eleven: Exercise 3 and 4 in the (random processes) notes; time for questions and brief midterm review.
robotics.eecs.berkeley.edu /~mayi/EECS226.html   (660 words)

 Registrar's Office | Fall 2005 Course Schedule | Applied Math
Emphasis on techniques of application rather than on rigorous mathematical demonstrationProbability, combinatorial probability, random variables, distribution functions, important probability distributions, independence, conditional probability, moments, covariance and correlation, limit theorems.
SHAPE AND GEOMETRY (3) Younes     Prereq: Calculus III and Linear Algebra   This class will review the basic definitions and properties of curves and surfaces, and their relation to the description and characterization of 2D and 3D shapes.
MATRIX ANALYSIS AND LINEAR ALGEBRA Fishkind Prereq: 110.405, Linear Algebra, multi-variable calculus.    A second course in linear algebra with emphasis on topics useful in analysis, economics, statistics, control theory, and numerical analysis.
www.jhu.edu /registrar/sched_crfall05/appliedmath.html   (1656 words)

 Algebra of random variables - Definition, explanation
77 codes by Volker Blobel for sorting, linear algebra, random number generation, least squares fitting with constraints and with many variables, and unfolding of measured distributions.
Fortran 77 codes by Volker Blobel for sorting, linear algebra, random number generation, least squares fitting with...
Help build the largest human-edited directory on the web.
www.calsky.com /lexikon/en/txt/a/al/algebra_of_random_variables.php   (337 words)

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