# Properties

 Label 0.1.2 Name $$\mu(2)$$ Weight $0$ Degree $1$ Real dimension $0$ Components $2$ Contained in $$\mathrm{O}(1)$$ Identity Component $$\mathrm{SO}(1)$$ Component group $$C_{2}$$

## Invariants

 Weight: $0$ Degree: $1$ $\mathbb{R}$-dimension: $0$ Components: $2$ Contained in: $\mathrm{O}(1)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{SO}(1)$ Index: $2$ $\mathbb{R}$-dimension: $0$ Description: $\mathrm{trivial}$

## Component Group

 Name: $C_{2}$ Order: $2$ Abelian: $\mathrm{True}$ Generators: $\left[\zeta_{2}\right]$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $1$ $0$ $1$ $0$ $1$ $0$ $1$ $0$ $1$

## Event Probabilities

 $\mathrm{P}[a_1=1]=\frac{1}{2}$ $\mathrm{P}[a_1=-1]=\frac{1}{2}$