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Some "mixed" distributions contain both stretches of continuous elementary events and some discrete elementary events; the discrete elementary events in such distributions can be called
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This example shows that, because the probability of each elementary event is zero, the probabilities assigned to elementary events do not determine a continuous
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682:
662:
383:. Elementary events and their corresponding outcomes are often written interchangeably for simplicity, as such an event corresponding to precisely one outcome.
334:
858:, the probability of an elementary event need not even be defined. In particular, the set of events on which probability is defined may be some
1066:
832:
probability distribution whose sample space is finite, each elementary event is assigned a particular probability. In contrast, in a
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898: – A measurable set with positive measure that contains no subset of smaller positive measure
828:
Elementary events may occur with probabilities that are between zero and one (inclusively). In a
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127:
151:
901:
895:
368:
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251:
156:
122:
16:"Basic outcome" and "Atomic event" redirect here. For atomic events in computer science, see
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8:
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distribution, individual elementary events must all have a probability of zero.
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27:
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1024:
922:
Wackerly, Denniss; William
Mendenhall; Richard Scheaffer (2002).
904: – Set of random variables of which any two are independent
575:{\displaystyle \{HH\},\{HT\},\{TH\},{\text{ and }}\{TT\}}
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if objects are being counted and the sample space is
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386:The following are examples of elementary events:
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953:(2nd ed.). New York: Springer. p. 9.
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1001:. San Diego: Academic Press. pp. 7–9.
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924:Mathematical Statistics with Applications
433:
977:
1078:
808:{\displaystyle S=(-\infty ,+\infty ).}
379:terminology, an elementary event is a
847:and can have non-zero probabilities.
1019:
999:Statistical Methods in Econometrics
490:{\displaystyle S=\{1,2,3,\ldots \}}
13:
971:
824:Probability of an elementary event
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787:
14:
1102:
950:Foundations of Modern Probability
637:{\displaystyle S=\{HH,HT,TH,TT\}}
440:{\displaystyle k\in \mathbb {N} }
1023:
41:
1086:Experiment (probability theory)
980:Concepts of Probability Theory
940:
915:
799:
781:
108:Collectively exhaustive events
1:
908:
882:and not necessarily the full
367:which contains only a single
1039:. You can help Knowledge by
7:
902:Pairwise independent events
889:
582:if a coin is tossed twice.
10:
1107:
1018:
978:Pfeiffer, Paul E. (1978).
15:
997:Ramanathan, Ramu (1993).
947:Kallenberg, Olav (2002).
817:probability distribution
278:Law of total probability
273:Conditional independence
162:Exponential distribution
147:Probability distribution
257:Conditional probability
1035:-related article is a
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809:
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709:{\displaystyle \{x\},}
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412:{\displaystyle \{k\},}
199:Continuous or discrete
152:Bernoulli distribution
982:. Dover. p. 18.
896:Atom (measure theory)
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664:stands for heads and
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157:Binomial distribution
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283:Law of large numbers
252:Marginal probability
177:Poisson distribution
26:Part of a series on
766:normal distribution
242:Complementary event
184:Probability measure
172:Pareto distribution
167:Normal distribution
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349:probability theory
293:Boole's inequality
229:Stochastic process
118:Mutual exclusivity
35:Probability theory
1091:Probability stubs
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1047:
875:{\displaystyle S}
856:probability space
852:measure-theoretic
753:{\displaystyle X}
729:{\displaystyle x}
677:{\displaystyle T}
657:{\displaystyle H}
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355:, also called an
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247:Joint probability
194:Bernoulli process
93:Probability space
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972:Further reading
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189:Random variable
140:Bernoulli trial
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18:linearizability
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1008:0-12-576830-3
1004:
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989:0-486-63677-1
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960:0-387-94957-7
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933:0-534-37741-6
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845:atomic events
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77:Indeterminism
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1041:expanding it
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949:
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827:
385:
373:sample space
361:sample point
360:
357:atomic event
356:
352:
346:
309:Tree diagram
304:Venn diagram
268:Independence
214:Markov chain
112:
98:Sample space
1033:probability
926:. Duxbury.
738:real number
224:Random walk
65:Determinism
53:Probability
1080:Categories
909:References
850:Under the
834:continuous
684:for tails.
377:set theory
135:Experiment
82:Randomness
28:statistics
884:power set
860:σ-algebra
797:∞
788:∞
785:−
687:All sets
482:…
430:∈
390:All sets
381:singleton
128:Singleton
890:See also
830:discrete
375:. Using
363:, is an
209:Variance
764:with a
740:. Here
371:in the
369:outcome
123:Outcome
1005:
986:
957:
930:
736:is a
716:where
644:where
419:where
70:System
58:Axioms
1031:This
841:atoms
760:is a
497:(the
365:event
351:, an
103:Event
1037:stub
1003:ISBN
984:ISBN
955:ISBN
928:ISBN
768:and
862:on
843:or
359:or
347:In
1082::
886:.
501:).
1068:e
1061:t
1054:v
1043:.
1011:.
992:.
963:.
936:.
870:S
819:.
803:.
800:)
794:+
791:,
782:(
779:=
776:S
748:X
724:x
704:,
701:}
698:x
695:{
672:T
652:H
632:}
629:T
626:T
623:,
620:H
617:T
614:,
611:T
608:H
605:,
602:H
599:H
596:{
593:=
590:S
570:}
567:T
564:T
561:{
553:,
550:}
547:H
544:T
541:{
538:,
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532:T
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526:{
523:,
520:}
517:H
514:H
511:{
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479:,
476:3
473:,
470:2
467:,
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461:{
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427:k
407:,
404:}
401:k
398:{
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
