From c54d169f6b91a19008ab10b2ffd4a2cb8bdb13f9 Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Mon, 8 Apr 2024 13:14:32 +1000
Subject: [PATCH 1/2] [lln_clt] Update editorial suggestions

Resolve most of the suggestions
---
 lectures/lln_clt.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/lectures/lln_clt.md b/lectures/lln_clt.md
index eaa05701..853f2e60 100644
--- a/lectures/lln_clt.md
+++ b/lectures/lln_clt.md
@@ -78,7 +78,7 @@ print(X)
 ```
 
 In this setting, the LLN tells us if we flip the coin many times, the fraction
-of heads that we see will be close to the mean $p$.
+of heads that we see will be close to the mean $p$. We use $n$ to represent the number of times the coin is flipped.
 
 Let's check this:
 
@@ -286,7 +286,7 @@ as expected.
 
 Let's vary `n` to see how the distribution of the sample mean changes.
 
-We will use a violin plot to show the different distributions.
+We will use a [violin plot](https://intro.quantecon.org/prob_dist.html#violin-plots) to show the different distributions.
 
 Each distribution in the violin plot represents the distribution of $X_n$ for some $n$, calculated by simulation.
 
@@ -357,7 +357,7 @@ This means that the distribution of $\bar X_n$ does not eventually concentrate o
 
 Hence the LLN does not hold.
 
-The LLN fails to hold here because the assumption $\mathbb E|X| = \infty$ is violated by the Cauchy distribution.
+The LLN fails to hold here because the assumption $\mathbb E|X| < \infty$ is violated by the Cauchy distribution.
 
 +++
 
@@ -438,7 +438,7 @@ Here $\stackrel { d } {\to} N(0, \sigma^2)$ indicates [convergence in distributi
 
 The striking implication of the CLT is that for **any** distribution with
 finite [second moment](https://en.wikipedia.org/wiki/Moment_(mathematics)), the simple operation of adding independent
-copies **always** leads to a Gaussian curve.
+copies **always** leads to a Gaussian(Normal) curve.
 
 
 
@@ -503,7 +503,7 @@ The fit to the normal density is already tight and can be further improved by in
 ```{exercise} 
 :label: lln_ex1
 
-Repeat the simulation [above1](sim_one) with the [Beta distribution](https://en.wikipedia.org/wiki/Beta_distribution).
+Repeat the simulation [above](sim_one) with the [Beta distribution](https://en.wikipedia.org/wiki/Beta_distribution).
 
 You can choose any $\alpha > 0$ and $\beta > 0$.
 ```

From ecaa6d86eea821098c19445df0f2f3d073151310 Mon Sep 17 00:00:00 2001
From: JingkunZhao <zhaojingkun1@gmail.com>
Date: Mon, 8 Apr 2024 18:08:37 +1000
Subject: [PATCH 2/2] Update lln_clt.md

---
 lectures/lln_clt.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/lectures/lln_clt.md b/lectures/lln_clt.md
index 853f2e60..7e7676ce 100644
--- a/lectures/lln_clt.md
+++ b/lectures/lln_clt.md
@@ -78,7 +78,9 @@ print(X)
 ```
 
 In this setting, the LLN tells us if we flip the coin many times, the fraction
-of heads that we see will be close to the mean $p$. We use $n$ to represent the number of times the coin is flipped.
+of heads that we see will be close to the mean $p$. 
+
+We use $n$ to represent the number of times the coin is flipped.
 
 Let's check this: