Summary table of probability terms: Difference between revisions

Revision as of 07:15, 1 January 2018

Summary table of probability terms

Term	Symbol	Type	Definition
Reals	$\mathbf {R}$
Borel subsets of the reals	${\mathcal {B}}$
Sample space	$\Omega$
Outcome	$\omega$	$\Omega$
Events	${\mathcal {F}}$
Probability measure	$\mathbf {P}$ or $\Pr$ or $\mathbf {P} _{\mathcal {F}}$	${\mathcal {F}}\to [0,1]$
Probability triple or probability space	$(\Omega ,{\mathcal {F}},\mathbf {P} )$
Distribution	$\mu$ or ${\mathcal {D}}$ or $D$ or $\mathbf {P} _{\mathcal {B}}$	${\mathcal {B}}\to \mathbf {[} 0,1]$	$B\mapsto \mathbf {P} (X\in B)$
Cumulative distribution function	$F_{X}$	$\mathbf {R} \to \mathbf {R}$
Density function	$f_{X}$	$\mathbf {R} \to \mathbf {R}$
Random variable	$X$	$\Omega \to \mathbf {R}$
Indicator of $A$	$1_{A}$	$\Omega \to \{0,1\}$
Expectation	$\mathbf {E}$ or $\mathrm {E}$	$(\Omega \to \mathbf {R} )\to \mathbf {R}$

@@ Line 20: / Line 20: @@
 | Probability triple or probability space || <math>(\Omega, \mathcal F, \mathbf P)</math> || ||
 |-
-| Distribution || <math>\mu</math> or <math>\mathcal D</math> or <math>D</math> or <math>\mathbf P_{\mathcal B}</math> || <math>\mathcal B \to \mathbf R</math> || <math>B \mapsto \mathbf P(X \in B)</math>
+| Distribution || <math>\mu</math> or <math>\mathcal D</math> or <math>D</math> or <math>\mathbf P_{\mathcal B}</math> || <math>\mathcal B \to \mathbf [0,1]</math> || <math>B \mapsto \mathbf P(X \in B)</math>
 |-
 | Cumulative distribution function || <math>F_X</math> || <math>\mathbf R \to \mathbf R</math> ||