Symbols:Greek/Beta
Beta
The $2$nd letter of the Greek alphabet.
- Minuscule: $\beta$
- Majuscule: $\Beta$
The $\LaTeX$ code for \(\beta\) is \beta .
The $\LaTeX$ code for \(\Beta\) is \Beta .
Beta Function
The Beta function $\Beta: \C \times \C \to \C$ is defined for $\map \Re x, \map \Re y > 0$ as:
- $\ds \map \Beta {x, y} := \int_{\mathop \to 0}^{\mathop \to 1} t^{x - 1} \paren {1 - t}^{y - 1} \rd t$
The $\LaTeX$ code for \(\map \Beta {x, y}\) is \map \Beta {x, y} .
Celestial Latitude
- $\beta$
Let $P$ be a point on the celestial sphere.
The celestial latitude of $P$ is the angle subtended by the the arc of the vertical circle through $P$ between $P$ and the ecliptic.
If $P$ is closer to the north ecliptic pole, the celestial latitude is defined as latitude $\beta \degrees$ north, where $\beta \degrees$ denotes $\beta$ degrees (of angle), written $\beta \degrees \, \mathrm N$.
If $P$ is closer to the south ecliptic pole, the celestial latitude is defined as latitude $\beta \degrees$ south, written $\beta \degrees \, \mathrm S$.
At the north ecliptic pole, the celestial latitude is $90 \degrees \, \mathrm N$.
At the south ecliptic pole, the celestial latitude is $90 \degrees \, \mathrm S$.
The $\LaTeX$ code for \(\beta\) is \beta .
Bohr Magneton: Variant
- $\beta$
The symbol for the Bohr magneton can also be seen presented as $\beta$.
Its $\LaTeX$ code is \beta .
Consumer's Risk
$\beta$
Consumer's risk is the probability that a consumer accepts a batch with a number of defectives which is unacceptable to that consumer.
The consumer's risk can be denoted by the symbol $\beta$ (beta).
The $\LaTeX$ code for \(\beta\) is \beta .
Probability of Type $\text {II}$ Error
- $\beta$
Used to denote the probability of a type $\text {II}$ error.
A type $\text {II}$ error is the failure to reject a false null hypothesis as the result of a hypothesis test.
The probability of a type $\text {II}$ error depends on the alternative hypothesis $H_1$, and for a particular $H_1$ is often denoted $\beta$.
The $\LaTeX$ code for \(\beta\) is \beta .
Linguistic Note
The Greek letter $\Beta$, $\beta$ (beta) is properly pronounced bee-ta, not the frequently-heard hypercorrection bay-ta.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Appendix $1$: Symbols and Conventions: Greek Alphabet