For questions involving the Rademacher distribution. Use this tag along with (probability-theory), or (probability).
Let $(\Omega, \mathscr F, \mathbb P)$ be a probability space with random variable $X$. $X$ has Rademacher distribution if $$P(X=1)=\frac12=P(X=-1)$$ or $$P(X=k)=\frac12 (\delta(k+1)+\delta(k-1))$$ for $k=\pm 1$ and $\delta$ is Dirac delta.
A series of Rademacher distributed variables can be regarded as a simple symmetrical random walk where the step size is 1.
It can be shown that $\frac{X+1}{2}$ has Bernoulli($\frac12$) distribution.