ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Collection of sets ▼ Set union ▼ Successor set ▼ Inductive set ▼ Set of inductive sets ▼ Set of natural numbers ▼ Set of integers ▼ Set of rademacher integers ▼ Rademacher integer ▼ Rademacher random integer ▼ Standard rademacher random integer ▼ Standard gaussian random real number
Definition D210
Gaussian random real number

Let $Z \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number.
A D3161: Random real number $X \in \text{Random}(\mathbb{R})$ is a gaussian random real number with parameters $\mu \in \mathbb{R}$ and $\sigma \in [0, \infty)$ if and only if $$X \overset{d}{=} \sigma Z + \mu$$
Children
 ▶ Folded gaussian random unsigned real number ▶ Log-gaussian random basic real number
Results
 ▶ Expectation of the absolute value of a centred gaussian random real number ▶ Finite sum of I.I.D. gaussian random real numbers is a gaussian random real number ▶ Finite sum of independent gaussian random real numbers is a gaussian random real number ▶ Finite sum of uncorrelated identically distributed gaussian random real numbers is a gaussian random real number ▶ Sample mean of I.I.D. gaussian random real numbers is a gaussian random real number ▶ Sample mean of independent gaussian random real numbers is a gaussian random real number ▶ Sample mean of uncorrelated identically distributed gaussian random real numbers is a gaussian random real number