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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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2 Answers 2

up vote 1 down vote accepted

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

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I like this idea as you've managed to one-line it. –  elleciel Feb 18 '13 at 23:13

How about using 2 cases? \begin{align} f(k)&=\cases{+2^k\qquad w.p.\;1/2\\-2^k\qquad w.p.\;1/2} \qquad k\in \text{Whatever} \end{align}

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Thanks for the suggestion. I was hoping for something more elegant but I'll give you an upvote once I have the reputation score >_<; –  elleciel Feb 18 '13 at 23:13

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