"Basic outcome" and "Atomic event" redirect here. For atomic events in computer science, see linearizability.
Part of a series on statistics
Probability theory
Probability
Axioms
Determinism
System
Indeterminism
Randomness
Probability space
Sample space
Event
Collectively exhaustive events
Elementary event
Mutual exclusivity
Outcome
Singleton
Experiment
Bernoulli trial
Probability distribution
Bernoulli distribution
Binomial distribution
Exponential distribution
Normal distribution
Pareto distribution
Poisson distribution
Probability measure
Random variable
Bernoulli process
Continuous or discrete
Expected value
Variance
Markov chain
Observed value
Random walk
Stochastic process
Complementary event
Joint probability
Marginal probability
Conditional probability
Independence
Conditional independence
Law of total probability
Law of large numbers
Bayes' theorem
Boole's inequality
Venn diagram
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In probability theory, an elementary event, also called an atomic event or sample point, is an event which contains only a single outcome in the sample space.[1] Using set theory terminology, an elementary event is a singleton. Elementary events and their corresponding outcomes are often written interchangeably for simplicity, as such an event corresponding to precisely one outcome.
The following are examples of elementary events:
All sets where if objects are being counted and the sample space is (the natural numbers).
if a coin is tossed twice. where stands for heads and for tails.
All sets where is a real number. Here is a random variable with a normal distribution and This example shows that, because the probability of each elementary event is zero, the probabilities assigned to elementary events do not determine a continuous probability distribution.
^Wackerly, Denniss; William Mendenhall; Richard Scheaffer (2002). Mathematical Statistics with Applications. Duxbury. ISBN 0-534-37741-6.
In probability theory, an elementaryevent, also called an atomic event or sample point, is an event which contains only a single outcome in the sample...
probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. The event A and its complement [not A] are mutually...
constitute an event, whereas outcomes with an odd number of pips may constitute another event. If the outcome is the element of the elementaryevent of two pips...
random variable. A random variable is a function that assigns to each elementaryevent in the sample space a real number. This function is usually denoted...
assumption of unit measure: that the probability that at least one of the elementaryevents in the entire sample space will occur is 1. P ( Ω ) = 1 {\displaystyle...
total probability of an outcome which can be realized via several distinct events, hence the name. The law of total probability is a theorem that states,...
space with elementaryevents {ω}, and let P be the probability measure with respect to the σ-algebra of Ω. Suppose we are told that the event B ⊆ Ω has...
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example...
set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2...
of the die if we look at it on the table without throwing it, each elementaryevent is reasoned deductively to have the same probability—thus the probability...
equally likely outcomes). In an elementary approach to probability, any subset of the sample space is usually called an event. However, this gives rise to...
probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes). Aside from the elementary work by Cardano...
of view, the events are nothing more than subsets, and the space of events is a Boolean algebra. We find elementary and compound events, exclusive and...
variables alternative hypothesis analysis of variance atomic event Another name for elementaryevent. bar chart Bayes' theorem Bayes estimator Bayes factor...
will be late. However, if a third event is introduced, person A and person B live in the same neighborhood, the two events are now considered not conditionally...
Determinism is the philosophical view that all events in the universe, including human decisions and actions, are causally inevitable. Deterministic theories...
random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the...
Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or are not caused deterministically. It is the opposite...
any event (set of outcomes), one can define a Bernoulli trial, corresponding to whether the event occurred or not (event or complementary event). Examples...
the most elementary levels, fence heights begin at around 18 inches to 2 ft (0.61 m). In Australia, where Equestrian Australia governs eventing competition...
The Sandy Hook Elementary School shooting was a mass shooting that occurred on December 14, 2012, in Newtown, Connecticut, United States, when 20-year-old...
elementary OS is a Linux distribution based on Ubuntu LTS. It promotes itself as a "thoughtful, capable, and ethical" replacement to macOS and Windows...
a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be...
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