Rademacher distribution

In probability theory and statistics, the Rademacher distribution (which is named after Hans Rademacher) is a discrete probability distribution where a random variate X has a 50% chance of being +1 and a 50% chance of being -1.

Rademacher

Support	${\displaystyle k\in \{-1,1\}\,}$
PMF	${\displaystyle f(k)=\left\{{\begin{matrix}1/2&{\mbox{if }}k=-1,\\1/2&{\mbox{if }}k=+1,\\0&{\mbox{otherwise.}}\end{matrix}}\right.}$
CDF	${\displaystyle F(k)={\begin{cases}0,&k<-1\\1/2,&-1\leq k<1\\1,&k\geq 1\end{cases}}}$
Mean	${\displaystyle 0\,}$
Median	${\displaystyle 0\,}$
Mode	N/A
Variance	${\displaystyle 1\,}$
Skewness	${\displaystyle 0\,}$
Ex. kurtosis	${\displaystyle -2\,}$
Entropy	${\displaystyle \ln(2)\,}$
MGF	${\displaystyle \cosh(t)\,}$
CF	${\displaystyle \cos(t)\,}$

A series (that is, a sum) of Rademacher distributed variables can be regarded as a simple symmetrical random walk where the step size is 1.