## Distribution of error with Bloom Filters

Let $S_1$ and $S_2$ be sets. Given a Bloom Filter $BF$ for fixed $m$ and $k$, then it's known that $\left|S_1 \cap S_2\right|$ can be estimated as

$\frac{\left|S_1\right|k\log\left(1-\frac{1}{m}\right)+\left|S_2\right|k\log\left(1-\frac{1}{m}\right)-\log\left(\left(1-\frac{1}{m}\right)^{\left|S_1\right|k}+\left(1-\frac{1}{m}\right)^{\left|S_2\right|k}+\frac{\text{BF}\left(S_1\right)\cdot\text{BF}\left(S_2\right)}{m}-1\right)}{k\log\left(1-\frac{1}{m}\right)}$

I'm trying to figure out how to calculate the error of this estimate. I'm having some trouble getting started since probability and statistics was never really my area of study. What do I need to figure out? How do I go about finding it?

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