Summary table of probability terms

Summary table of probability terms

Table

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

See also

• Comparison of machine learning textbooks