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Updates from Overleaf
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japm48 committed Jun 4, 2023
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10 changes: 5 additions & 5 deletions main.tex
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Expand Up @@ -134,7 +134,7 @@ \section*{References}
% TODO: add McEliece book !!
\item Raymond W.\@ Yeung, \emph{Information Theory and Network Coding}, 1st ed., ISBN: 978-0-387-79234-7, CUHK.
1
\item
Akshay Krishnamurthy, Aarti Singh, \emph{10-704 Lecture Notes}, Winter 2016-2017, CMU.
\\
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\quad
Y_N \xrightarrow[]{P} \mathbb{E}[X]
\\
Convergence in probability:
& \text{[TODO]}
\\
%Convergence in probability:
%& \text{[TODO]}
%\\
Central Limit Theorem (CLT): & Y_N = \frac{1}{N}\sum_{i=1}^{N} X_i \quad (X_i \text{ i.i.d., } \mathbb{E}[X_i] = \mu,\,\mathbb{V}[X_i]=\sigma^2)
\\&
\frac{Y_N-\mu}{\sigma/\sqrt{N}}
Expand All @@ -307,7 +307,7 @@ \subsection*{Basic properties}
\\
Log-sum inequality: & \sum_i a_i \cdot \log \frac{a_i}{b_i} \ge
A \cdot \log \frac{A}{B}; \quad A =\sum_i a_i; \, B =\sum_i b_i; \, a_i\ge 0,\,b_i\ge 0
A \cdot \log \frac{A}{B}; \quad A =\sum_i a_i; \, B =\sum_i b_i; \, a_i > 0,\,b_i > 0
\\
IT inequality: & \log_B (r) \le (r-1)\cdot \log_B(e); \\[-10pt]&
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