Summary table of probability terms

Summary table of probability terms

Table

Term	Symbol	Type
Reals	$\mathbf {R}$
Borel subsets of the reals	${\mathcal {B}}$
Sample space	$\Omega$
Outcome	$\omega$	$\Omega$
Events	${\mathcal {F}}$
Probability measure	$\mathbf {P}$ or $\Pr$	${\mathcal {F}}\to [0,1]$
Probability triple or probability space	$(\Omega ,{\mathcal {F}},\mathbf {P} )$
Distribution	$\mu$ or ${\mathcal {D}}$ or $D$	${\mathcal {B}}\to \mathbf {R}$
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 $\mathrm {E}$	$(\Omega \to \mathbf {R} )\to \mathbf {R}$