eth-janishutz/eth-summaries
1
0
Fork 0
mirror of https://github.com/janishutz/eth-summaries.git synced 2026-07-27 09:14:38 +02:00
Code Issues Packages Projects Releases Wiki Activity

[AW] Fix error in chebyshev inequality, fixes #7

Browse Source
This commit is contained in:
janishutz
2026-07-15 14:21:31 +02:00
parent ff9258fb22
commit 6b48b32b7d
2 changed files with 1 additions and 1 deletions
Download Patch File Download Diff File Expand all files Collapse all files
semester2/algorithms-and-probability/aw-summary.pdf
BIN
View File
Binary file not shown.
semester2/algorithms-and-probability/parts/probability/approximating-probabilities.tex
+1 -1
View File
@@ -15,7 +15,7 @@ Markov's inequality is fairly straight forward to prove, and it already allows u
\begin{theorem}[]{Chebyshev's inequality}
Let $\mathcal{X}$ be a random variable and $t > 0 \in\R$. Then we have
\begin{align*}
\Pr[|\mathcal{X} - \E[\mathcal{X}| \geq t]] \leq \frac{\text{Var}[\mathcal{X}]}{t^2} \Longleftrightarrow \Pr[|\mathcal{X} - \E[\mathcal{X}]| \geq t \cdot \sqrt{\text{Var}[\mathcal{X}]}] \leq \frac{1}{t^2}
\Pr[|\mathcal{X} - \E[\mathcal{X}]| \geq t] \leq \frac{\text{Var}[\mathcal{X}]}{t^2} \Longleftrightarrow \Pr[|\mathcal{X} - \E[\mathcal{X}]| \geq t \cdot \sqrt{\text{Var}[\mathcal{X}]}] \leq \frac{1}{t^2}
\end{align*}
\end{theorem}