Sample space

event spacespacerepresented by pointssample spaces
In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.wikipedia
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Probability theory

theory of probabilityprobabilityprobability theorist
In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.
Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Experiment (probability theory)

experimentrandom experimentrandom experiments
In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space.

Outcome (probability)

outcomeoutcomesequally likely outcomes
In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.
All of the possible outcomes of an experiment form the elements of a sample space.

Event (probability theory)

eventeventsrandom event
A subset of the sample space is an event, denoted by E. Referring to the experiment of tossing the coin, the possible events include E={H} and E={T}. A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).
In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

Probability space

probability measuresGaussian measureoutcomes
A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

Sigma-algebra

σ-algebraσ-algebrasigma algebra
A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).
This means the sample space Ω must consist of all possible infinite sequences of H or T:

Trial and error

trial-and-errorgenerate and test trial and error principle
In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.

Set (mathematics)

setsetsmathematical set
In probability theory, the sample space (also called sample description space or possibility space ) of an experiment or random trial is the set of all possible outcomes or results of that experiment.

Set notation

notational motivationsthe broader class of means of denoting sets
A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set.

Element (mathematics)

elementelementsset membership
A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set.

Universe (mathematics)

universeuniversal setdomain
It is common to refer to a sample space by the labels S, Ω, or U (for "universal set").

Dice

dieDice rollingpolyhedral dice
For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).

Probability

probabilisticprobabilitieschance
A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

Probability measure

measureprobability distributionlaw
A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

Playing card

playing cardscardscard
For example, when drawing a card from a standard deck of fifty-two playing cards, one possibility for the sample space could be the various ranks (Ace through King), while another could be the suits (clubs, diamonds, hearts, or spades).

Playing card suit

suitsuitscard suit
For example, when drawing a card from a standard deck of fifty-two playing cards, one possibility for the sample space could be the various ranks (Ace through King), while another could be the suits (clubs, diamonds, hearts, or spades).

Cartesian product

productCartesian squareCartesian power
A more complete description of outcomes, however, could specify both the denomination and the suit, and a sample space describing each individual card can be constructed as the Cartesian product of the two sample spaces noted above (this space would contain fifty-two equally likely outcomes).

Drawing pin

thumbtackthumbtacksthumb tack
However, there are experiments that are not easily described by a sample space of equally likely outcomes—for example, if one were to toss a thumb tack many times and observe whether it landed with its point upward or downward, there is no symmetry to suggest that the two outcomes should be equally likely.

Statistics

statisticalstatistical analysisstatistician
In statistics, inferences are made about characteristics of a population by studying a sample of that population's individuals.

Statistical population

populationsubpopulationsubpopulations
In statistics, inferences are made about characteristics of a population by studying a sample of that population's individuals.

Sample (statistics)

samplesamplesstatistical sample
In statistics, inferences are made about characteristics of a population by studying a sample of that population's individuals.

Bias of an estimator

unbiasedunbiased estimatorbias
In order to arrive at a sample that presents an unbiased estimate of the true characteristics of the population, statisticians often seek to study a simple random sample—that is, a sample in which every individual in the population is equally likely to be included.