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Topic: Sample space

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	Probability Models (Probability Central)
		The sample space is often presented by the letter S.
		An event is the set of outcomes of a random phenomenon, that is, a subset of a sample space.
		When asking four people to vote on a subject, assume the sample space, S, for all four votes is the list of all possible outcomes in the form of two affirmatives.
	library.thinkquest.org /11506/pmodels.html (476 words)

	tScholars.com \| Sample space (Site not responding. Last check: )
		In probability theory, the sample space or universal sample space, often denoted S, Ω or U (for "universe"), of an experiment or random trial is the set of all possible outcomes.
		Sample spaces appear naturally in an elementary approach to probability, but are also important in probability spaces.
		A probability space (Ω, F, P) incorporates a sample space of outcomes, Ω, but defines a set of events of interest, the σ-algebra F, for which the probability measure P is defined.
	www.tscholars.com /encyclopedia/Sample_space (269 words)

	Sample space (Site not responding. Last check: )
		Anysubset of the sample space is usually called an event, while subsets of the sample space containing just a single element are called elementary events.
		Sample spaces appear naturally in an elementary approach to probability,but are also important in probability spaces.
		A probability space(Ω, F, P) incorporates a sample space of outcomes, Ω, but defines a set of events ofinterest, the σ-algebra F, for which the probability measure P is defined.
	www.therfcc.org /sample-space-8851.html (228 words)

	NationMaster - Encyclopedia: Probability space
		In mathematics, a probability space or probability measure is a set S, together with a σ-algebra X on S and a measure P on that σ-algebra such that P(S) = 1.
		The set S is called the sample space and the elements of X are called the events.
		We call this sort of probability space a continuous probability space and are lead to questions in measure theory when we try to define P. random variable is a measureable function on Ω.
	www.nationmaster.com /encyclopedia/Probability-space (481 words)

	Sample space - Glasgledius (Site not responding. Last check: )
		Each element in the sample space is called an elementary event, while every subset of the sample space is called simply an event.
		For example, when drawing a card from a standard deck of 52 playing cards, one sample space could be the rank (Ace through King) and another could be the suit (clubs, diamonds, hearts, or spades).
		Although the sample spaces are independent, some assignments of probabilities to points may lead to a circumstance in which the random variables thus defined are not describable as independent.
	www.glasglow.com /E2/pr/Probability___Sample_space.html (231 words)

	Math Forum: Ask Dr. Math FAQ: Probability in the Real World
		If our meteorologist has data for 100 days with similar weather conditions (the sample space and therefore the denominator of our fraction), and on 70 of these days it rained (a favorable outcome), the probability of rain on the next similar day is 70/100 or 70%.
		The sample space is the total number of at-bats a player has had, not including walks.
		The sample space, however, is quite large because it is equal to 49_P_6, which is roughly 10 billion.
	www.mathforum.org /dr.math/faq/faq.prob.world.html (1142 words)

	Section 6.3
		A sample space is a way to break down an event from which we can record observations upon.Suppose we were to experiment with trying to predict gas price fluctuations of a gas station "X" from a nearby service station "Y".
		Our sample space might be a range of values from say.95 to 1.50.
		The key point is that simple events are represented as elements of the sample space while compound events are representative of subsets of the sample space.
	www.msu.edu /~osstutor/63_s_110.htm (286 words)

	Sample Space
		When we say that tossing one coin has a sample space of {H, T}, we are saying that the outcome could be either H (heads) or T (tails).
		{R,G,B} The concept of a sample space seems to work well for processes where the outcomes are discrete, which means that the outcomes can be clearly defined and distinguished from one another.
		The dart could land at a distance of 2 centimeters, or 2.2 centimeters, or 2.22 centimeters, etc. This poses a problem for defining the sample space.
	arnoldkling.com /apstats/samplespace.html (296 words)

	CCD Students Beam Up Questions To Space Station (Site not responding. Last check: )
		With the help of Charlie Sufana, their Amateur Radio on the International Space Station liaison/mentor, they were to use a telebridge system to dial up astronaut Bill McArthur and chat with him about life on the International Space Station.
		McArthur, who has been aboard the space station since October, will be orbiting the earth as he talks to the students.
		They'll start their assembly by going outside to launch their model rocket of the space shuttle before being beamed up to the space station.
	www.ham-shack.com /passiton/students_beam_up_questions.html (434 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		For many standard probability distributions, such as the normal distribution the sample space is the set of real numbers or some subset of the real numbers.
		In the general measure-theoretic description of probability spaces, an event may be defined as an element of a selected σ-algebra of subsets of the sample space.
		Under this definition, any subset of the sample space that is not an element of the σ-algebra is not an event, and does not have a probability.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=event_(probability_theory) (493 words)

	NationMaster - Encyclopedia: Loss function
		In statistics, decision theory and economics, a loss function is a function that maps an event (technically an element of a sample space) onto a real number representing the economic cost or regret associated with the event.
		Combining the three elements of the prior probability, the data, and the loss function then allows decisions to be based on maximising the subjective expected utility, a concept introduced by Leonard J. Savage.
		Dina statistik, decision theory sarta ékonomi, a loss function is a function that maps an event (technically an element of a sample space) onto a real number representing the economic cost or regret associated with the event.
	www.nationmaster.com /encyclopedia/Loss-function (634 words)

	Univariate Statistics - Distributions and Hypotheses
		A sampling distribution can be defined as a theoretical probability distribution of all possible values of a sample statistic which would occur if all possible samples of size N were drawn from the population.
		In order to describe any sampling distribution which is represented by a continuous curve, we need three pieces of inofrmation: the mean, the sample, size, and the standard deviation.
		The sampling distribution can then be used in order to make determinations about the probability of an expected outcome, even in cases where the exact sampling distribution is not known.
	www.uwsp.edu /psych/cw/statmanual/distribute.html (1184 words)

	History, Well Sample and Core Library, Kentucky Geologic Survey
		Samples were first collected during the 1920's and stored at the Survey offices, which were located in the center of the University of Kentucky campus.
		Sample space was increased by 1,312 square feet in 1972, core space was increased by 1,458 square feet in 1975, and sample space was again increased by 1,968 square feet in 1978.
		The KGS Well Sample and Core Library was moved during April and May of 1995 to a temporary location at 554 South Forbes Road, Warehouse 23, occupying 60,000 square feet of space, until a proposed new, permanent facility could be built in about 2 years.
	www.uky.edu /KGS/core_library/history.htm (892 words)

	Probability.html
		To describe sample spaces in such a way that each outcome is equally likely you must sometimes distinguish between various outcomes in ways that appear artificial.
		Because the number of outcomes in an event must be less than or equal to the number of outcomes in the sample space (this is because the event is a subcollection of the sample space), the probability of an event must be a number between 0 and 1.
		The complement of an event A is the collection of all outcomes in the sample space that are not in A. The complement of A is denoted by A'.
	www.marlboro.edu /academics/study/mathematics/courses/probability.html (2464 words)

	String Theory from Sample space
		The basic premise is that a mathematical description of logic is accomplished by the union and intersection of regions of sample space.
		Whatever dimensionality the manifold of reality has, a region of this sample space is described by a hypersurface that is itself a manifold of one dimension less then the original space.
		Whatever the dimensionality of the sample space, 3 dimensions are required to represent a region of sample space prevented from being completely closed by a continuous edge.
	www.sirus.com /users/mjake/StringTh.html (2627 words)

	Grade 6: Statistics and Probability: When Students Ask
		To be sure your sample is not biased and truly reflects the population under consideration, you need to ensure that every subject in the population had an equal chance of being selected.
		The sample that was used in the poll came from a subset of people who owned telephones and thus did not reflect the total voting population, since many voters then did not own telephones.
		In this sample space each of the outcomes is equally likely, and we can determine from it that the probability of the event of tossing exactly 2 heads is 3/8.
	www.eduplace.com /math/mw/background/6/11/te_6_11_stats_ask.html (399 words)

	Introduction to Probability
		A sample space is the set of all possible outcomes.
		When writing the sample space, it is highly desirable to have events which are equally likely.
		The probability of an event occurring is the number in the event divided by the number in the sample space.
	www.richland.edu /james/lecture/m113/probability.html (397 words)

	Fundamentals
		A sample space is a specification of all the outcomes that might result from an action taken, a decision made, or an experiment performed.
		If every point in the sample space is contained in at least one member of a family of events, then the family of events is called totally exhaustive.
		The sample spaces and probabilities for which this is true can be quite ordinary, but the "non-probalizable" subsets are weird, and don't have any engineering significance (probably and hopefully).
	www.ceet.niu.edu /faculty/marcellus/Probabilitarium/Library/RefFundamentals.html (1173 words)

	sample space
		Abacci > Abaccipedia > sa > sample space
		In probability theory, the sample space, often denoted S, Ω or U (for "universe"), of an experiment or random trial is the set of all possible outcomes.
		For tossing a single die, the sample space is {1, 2, 3, 4, 5, 6}.
	www.abacci.com /wikipedia/topic.aspx?cur_title=sample_space (332 words)

	SPACE.com -- How Genesis Crash Impacts Mars Sample Return
		The return sample canister was banged up and severely damaged by the high-speed impact, leaving scientists to pluck through trashed and twisted hardware in the hopes of salvaging science data.
		Seeing that the Genesis sample canister was breached and its contents exposed to Earth's biosphere, "the Mars Sample Return mission needs to be rethought entirely," said Barry DiGregorio, a research associate with the Cardiff Center for Astrobiology in the United Kingdom.
		DiGregorio is also director for the International Committee Against Mars Sample Return (ICAMSR), an activist group established to increase public awareness regarding Mars-to-Earth transit of samples, along with any possible negative consequences that could occur due to an MSR canister either becoming opened unintentionally on impact, or lost during entry into the Earth's atmosphere.
	www.space.com /missionlaunches/mars_genesis_040916.html (1527 words)

	Probability (Site not responding. Last check: )
		Sample space is the set of all possible outcomes for an experiment.
		Find the sample space of selecting a four-digit personal identification number for an ATM card.
		Find the sample space of drawing two cards from a standard deck of fifty-two cards.
	www.gomath.com /htdocs/lesson/probability_lesson5.htm (202 words)

	UOR_2.1
		As these three examples indicate, the number of elements or points in a sample space can be finite, countably infinite, or noncountably infinite.
		For this, we require knowledge of the algebra of events, where an event is defined to be a collection of points in the sample space.
		An event containing no points in the sample space is called o, the empty event (or null set).
	web.mit.edu /urban_or_book/www/book/chapter2/2.1.html (878 words)

	Math Forum: Ask Dr. Math FAQ: Probability
		In our problem, the sample space consists of all ten marbles in the jar, because we are equally likely to draw any one of them.
		The sample space is a set consisting of all the possible outcomes of an event (like drawing a marble from a jar, or picking a card from a deck).
		Because each probability is a fraction of the sample space, the sum of the probabilities of all the possible outcomes equals one.
	mathforum.org /dr.math/faq/faq.prob.intro.html (1086 words)

	Geometric Distribution (Site not responding. Last check: )
		We begin with a sample space for the experiment, a set of all the possible outcomes from the experiment.
		Now we can assign probabilities to the sample points, using the fact that the trials are independent (so the probabilities of single trials are multiplied to give the probabilities of the events).
		This is as it should be; we have assigned a total probability of 1 to the entire sample space.
	www.rose-hulman.edu /math21st/lectures/GD/GD_2.html (227 words)

	Microsoft Visio 2002: Space Plan Technical Overview (Site not responding. Last check: )
		Visio Space Plan is customizable to the degree that it can produce a space plan or a report that matches the data you import from your data source.
		Space ID field The Space ID field is used to create an association between a space on your plan and the other shapes that can be added to that space.
		Space ID The data from your source file that you map to this field should uniquely identify the category you are creating.
	www.microsoft.com /technet/prodtechnol/Visio/visio2002/maintain/spacepln.mspx (5404 words)

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