From 1cebd490395f8ae2fd64a67c0783cbc06f6f3ef0 Mon Sep 17 00:00:00 2001 From: japm48 Date: Sun, 4 Jun 2023 01:58:30 +0200 Subject: [PATCH] Updates from Overleaf --- main.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/main.tex b/main.tex index 68c0f5b..f369e5f 100644 --- a/main.tex +++ b/main.tex @@ -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. \\ @@ -287,9 +287,9 @@ \subsection*{Basic properties} \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}} @@ -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]&