Summary table of probability terms: Difference between revisions

Revision as of 07:14, 1 January 2018

Summary table of probability terms

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

@@ Line 16: / Line 16: @@
 | Events || <math>\mathcal F</math> || ||
 |-
-| Probability measure || <math>\mathbf P</math> or <math>\Pr</math> || <math>\mathcal F \to [0,1]</math> ||
+| Probability measure || <math>\mathbf P</math> or <math>\Pr</math> or <math>\mathbf P_{\mathcal F}</math> || <math>\mathcal F \to [0,1]</math> ||
 |-
 | 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> || <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 R</math> || <math>B \mapsto \mathbf P(X \in B)</math>
 |-
 | Cumulative distribution function || <math>F_X</math> || <math>\mathbf R \to \mathbf R</math> ||