# Notation for probability of either sign

I have a function $f(k) = \pm 2^k$ with probability $1/2$ of either sign. How would I express this in a cleaner notation? I'm guessing to use the Kronecker delta somehow, but I can't put a finger on it.

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You might try $f(k)=2^kX_k$ where $X_k$ is a symmetric Bernoulli random variable (this means that $\mathbb P(X_k=+1)=\mathbb P(X_k=-1)=\frac12$).