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Topic: Joint probability

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	Univariate Statistics - Intermediate Probability
		The joint probability, then, can be determined by dividing the number of individuals within the cell by the total number of individuals.
		Thus, the conditional probability is simply the joint probability divided by the marginal probability.
		The notion of conditional probability is a very important one, perhaps one of the most useful in probability theory for research purposes.
	www.uwsp.edu /psych/cw/statmanual/probinter.html (1039 words)

	Probability - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-19)
		probability is taken as a primitive (that is, not further analyzed) and the emphasis is on constructing a consistent assignment of probability values to propositions.
		Probability applications include even more than statistics, which is usually based on the idea of probability distributions and the central limit theorem.
		Governments typically apply probability methods in environment regulation where it is called "pathway analysis", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on their perceived probable effect on the population as a whole, statistically.
	encyclopedia.worldsearch.com /probability.htm (2624 words)

	Bayesian probability (Site not responding. Last check: 2007-10-19)
		Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of statements, or to the degree of belief of rational agents in the truth of statements; when used with Bayes theorem, it then becomes Bayesian inference.
		This is in contrast to frequentism, which rejects degree-of-belief interpretations of mathematical probability, and assigns probabilities only to random events according to their relative frequencies of occurrence.
		The Bayesian approach is in contrast to the concept of frequency probability where probability is held to be derived from observed or imagined frequency distributions or proportions of populations.
	hallencyclopedia.com /Bayesian_probability (1288 words)

	Methods and systems for extracting a joint probability from a map decision device and processing a signal using the ... (Site not responding. Last check: 2007-10-19)
		In addition, backward state probabilities through the k-th stage of the trellis are calculated and branch probabilities are calculated between a state at the (k-n)-th stage of the trellis and a state at the k-th stage of the trellis.
		The joint probability information is generated from a MAP decision device by selecting a first one of the received symbols and a second one of the received symbols.
		Probability information associated with the first symbol and the second symbol is obtained from the MAP decision device and a joint probability of the first symbol and the second symbol is determined from the obtained probability information associated with the first symbol and the second symbol.
	www.patentstorm.us /patents/6798852.html (10553 words)

	Joint Distributions
		This activity will help clarify the concept of a joint probability density function and examine how to use this function to determine marginal and conditional distributions.
		Understand the relationship of marginal and conditional distributions to both the joint distribution and the probability distributions of the component random variables.
		Find the probability that the sum of the life expectancies is at least 3.
	www.saintmarys.edu /~psmith/345act9.html (639 words)

	Probability (Site not responding. Last check: 2007-10-19)
		If the probability of the found distribution is quite low given that the die is fair, then you may reject the hypothesis that the die is fair, and consequentially conclude that the die is biased.
		The probability of either of two events A or B occurring is the probability of event A plus the probability of event B minus the probability that both A and B will occur.
		The binomial probability distribution arises in any situation where there are: (1) only two possible outcomes, (2) the number of trials or observations is fixed, (3) all the observations are independent, and (4) the probability of a success (p) is identical for each observation.
	espse.ed.psu.edu /statistics/Chapters/Chapter7/Chap7.html (4439 words)

	6. Bivariate Rand. Vars.
		In the discrete case conditional probabilities are found by restricting attention to rows or columns of the joint probability table.
		The technique shown above for a conditional probability in the discrete case doesn't carry over to the continuous case because the 'row' (the probability of a specific value of X) and 'column' (the probability of a specific value of Y) totals are zero in the continuous case.
		From exercise 5.8 in that section, the joint density function of X and Y is f(x,y) = 2 when x is on the interval [0,1], y is on the interval [0,1], and x+y is on the interval [0,1].
	www.csus.edu /indiv/j/jgehrman/courses/stat50/bivariate/6bivarrvs.htm (2045 words)

	Conditional probability -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		Conditional probability is the (A measure of how likely it is that some event will occur) probability of some (Something that happens at a given place and time) event A, assuming event B.
		The joint probability of A and B is written or
		Conditional probability is more easily calculated with a (additional info and facts about decision tree) decision tree.
	www.absoluteastronomy.com /encyclopedia/c/co/conditional_probability.htm (308 words)

	UNC Image Processing Software (Site not responding. Last check: 2007-10-19)
		Joint entropy is computed using the same formula, except that h(i) is a slot in the joint histogram computed for the two images.
		In other words, p(i) is the probability that a pixel in first image has a certain intensity and that the same pixel in the second image has some certain value.
		That is, for each input pixel, the output is the entropy (individual or joint), joint probabil- ity or mutual information of the input pixel or pixels.
	www.cs.unc.edu /~fritsch/html/entropy.1I.html (552 words)

	Lecture Notes 4 (Site not responding. Last check: 2007-10-19)
		A probability is expressed as a decimal, such as 0.7 or as a fraction, such as 7/10, or as percentage, such as 70%.
		A joint probability is denoted by P(X and Y).
		An example of conditional probability is the probability that a person wears glasses given that she is blond.
	business.clayton.edu /arjomand/business/l4.html (2211 words)

	Probability - Open Encyclopedia (Site not responding. Last check: 2007-10-19)
		As with the theory of mechanics which assigns precise definitions to such everyday terms as work and force, so the theory of probability attempts to quantify the notion of probable.
		Peters's (1856) formula for $r, the$ probable error of a single observation, is well known.
		The probability of an event is generally represented as a real number between 0 and 1.
	open-encyclopedia.com /Probability (2628 words)

	Joint Probability
		This type of probability depends on whether the experiment is done with or without replacement.
		The probability that independent events A and B happen simultaneously is found by using the
		The probability of drawing the second queen is also 4/52 and the third is 4/52.
	math.youngzones.org /joint.html (434 words)

	Joint probability of precipitation and discharge deficits in the Netherlands
		Joint probability of precipitation and discharge deficits in the Netherlands
		In addition, nearest-neighbor resampling is used to estimate joint probabilities of precipitation and discharge deficits.
		Nearest-neighbor resampling also underestimates this probability, mainly because the upper tails of the marginal distributions are not properly reproduced by the simulations.
	www.agu.org /pubs/crossref/2004/2004WR003265.shtml (314 words)

	Uncertainty and probabilistic reasoning
		Probabilities can be used to describe the agent's degree of belief in a sentence.
		The probability of any statement involving the random variables can be calculated from their joint probability distribution.
		The joint probability distribution is written as follows (notice the capital P to distinguish it fromt the probability of an atomic event, the assignment of values to all the variables.)
	www.sdsc.edu /~tbailey/teaching/cse151/lectures/chap14.html (841 words)

	Joint events
		Note that in equation (3) the terms on the right are simply alternative means of representing the joint event symbolically, and equation (4) simply gives the rule for combining the probabilities of component events to obtain the probability of the joint event.
		The conditional probability is therefore 1/52 divided by 1/13 or 1/4, as of course it should be.
		The relationship given by equation (5) is not only the means of determining a conditional probability, it is also the means of converting a series of known conditional probabilities into the solution of an unknown one.
	web.nmsu.edu /~brook/courses/handouts/probability/node4.html (566 words)

	Probability of A and B (1 of 2) (Site not responding. Last check: 2007-10-19)
		Probability of A and B (1 of 2)
		Since the probability of each event is 1/2, the probability of both events is: 1/2 x 1/2 = 1/4.
		What is the probability that the first card is the ace of clubs and the second card is a club (any club).
	www.ruf.rice.edu /~lane/hyperstat/A127969.html (212 words)

	FTC Office of the General Counsel - Amicus Briefs
		Joint brief of the United States and the Federal Trade Commission, as amici curiae, addressing the proper application of the Foreign Trade Antitrust Improvements Act where a foreign plaintiff's claimed injury from an alleged antitrust conspiracy does not arise from the effects of that conspiracy on U.S. commerce.
		Joint brief of the United States, the Federal Trade Commission, and the Patent and Trademark Office, as amici curiae, urging the Court to reverse the ruling of the court of appeals, which was based on a presumption that the possession of a patent conveys market power for purposes of adjudicating a claim of tying.
		Joint amicus brief of the United States and the Federal Trade Commission, urging the Georgia Supreme Court to reject a ruling by the Georgia State Bar Standing Committee on the Unlicensed Practice of Law, which had determined that real estate closings must be conducted by licensed attorneys.
	ftc.gov /ogc/briefs.shtm (4078 words)

	Joint Marginal and Conditional
		Joint probability is the probability of two or more things happening together.
		The marginal probability is determined from the joint distribution of x and y by integrating over all values of y, called "integrating out" the variable y.
		Note that in general the conditional probability of A given B is not the same as B given A. The probability of both A and B together is P(AB), and P(AB) X P(B) = P(AB) = P(BA) X P(A), if both P(A) and P(B) are non-zero.
	www.statisticalengineering.com /joint_marginal_conditional.htm (486 words)

	Stats: Probability Rules
		If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.
		The 0.14 is because the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14.
		This means that the probability of B occurring, whether A has happened or not, is simply the probability of B occurring.
	www.richland.edu /james/lecture/m170/ch05-rul.html (542 words)

	Graphical Models
		Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data.
		By the chain rule of probability, the joint probability of all the nodes in the graph above is
		Unfortunately, the method of first computing the full joint probability distribution, and then marginalizing out the unwanted nodes, takes time which is exponential in the number of nodes.
	www.cs.ubc.ca /~murphyk/Bayes/bayes.html (6598 words)

	ONLamp.com -- Calculating Entropy for Data Miners
		The main difference is that the joint entropy formula has two summation signs instead of one, and the probability distribution being summed over is a joint probability distribution instead of a univariate probability distribution.
		It outputs a joint frequency table, a joint probability table, and the summary joint entropy score.
		The calculation of the joint entropy score is the same as the calculation of the univariate entropy score.
	www.onlamp.com /pub/a/php/2005/03/24/joint_entropy.html (620 words)

	Conditional probability Article, Conditionalprobability Information (Site not responding. Last check: 2007-10-19)
		That is, it is the probability of bothevents together.
		Marginal probability is the probability of one event, ignoring any information about the other event.Marginal probability is obtained by summing (or integrating, more generally) the joint probability over the ignored event.
		Themarginal probability of A is written P(A), and the marginal probability of B is writtenP(B).
	www.anoca.org /event/written/conditional_probability.html (252 words)

	ipedia.com: Probability Article (Site not responding. Last check: 2007-10-19)
		Informally, probable is one of several words applied to uncertain events or knowledge, being more or less interchangeable with likely, risky, hazar...
		Probability theory, as applied to observations, was largely a nineteenth century development.
		Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions of use in these types of problems only arose much later.
	www.ipedia.com /probability.html (2519 words)

	Joint Distributions 10/19, 10/20
		In general, when we build the joint distribution of two random variables we can make such a two-way table, of course, for more variables this is impossible.
		In the case of two random variables X and Y we define the joint probability mass function of X and Y as :
		In general, given the joint distribution on the pairs (x,y) for two random variables X and Y: P(x,y) we have the marginal distributions
	www-stat.stanford.edu /~susan/courses/s116/node65.html (306 words)

	S.O.S. Mathematics CyberBoard :: View topic - Joint probability distributions
		If the joint probability distribution of X and Y is given by f(x, y) = c(x^2 + y^2) for x = -1, 0, 1, 3; y = -1, 2, 3, find the value of c.
		To find the value of c, use the fact that the probabilities must add to 1 for the twelve ordered pairs for which the probability is positive.
		The joint density is constant over a triangular region, and in fact is the reciprocal of the area of the triangle in the first quadrant.
	www.sosmath.com /CBB/viewtopic.php?t=2615&start=0&postdays=0&postorder=asc&highlight= (289 words)

	AMS 311 (Site not responding. Last check: 2007-10-19)
		Consider a circle of radius R and suppose that a point within the circle is randomly chosen in such a manner that all regions within the circle of equal area are equally likely to contain the point.
		Joint cdf is product of marginal cdfs for independent random variables.
		Joint pdf (pmf) is a product of marginal pdfs (pmfs) for independent random variables.
	www.ams.sunysb.edu /~dorothy/handout20.html (480 words)

	Stats: Conditional Probability
		Recall that the probability of an event occurring given that another event has already occurred is called a conditional probability.
		This is because they are conditional probabilities and the table is a joint probability table.
		However, and I hope you agree, it is much easier to take the joint probability divided by the marginal probability.
	www.richland.edu /james/lecture/m170/ch05-cnd.html (860 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		Event: Snow storm Outcomes: Class cancelled 0.10 Class not cancelled 0.90 1.00 Three types of probabilities: Marginal: General probabilities Joint: Two outcomes occurring simultaneously (compound outcomes) Conditional: Probability of an outcome occurring if a particular outcome has already occurred.
		Independent Situations: Joint Probabilities: Product of the two marginal probabilities (only if the two outcomes are independent) i.e.
		Equal to the Probability of branch to the left * the joint Probability of circle to the left of the branch 1 6>l~¦®ÐÕÆÞßòOhy¤¥·ÂÆÉÓÔìí .
	www.physics.mun.ca /~cdeacon/business/b2401/extranotes/Chapter10Notes.doc (211 words)

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