From aeb5314b8bd7a42d391d59c020dd9f6ca127a67b Mon Sep 17 00:00:00 2001
From: Arthur DANJOU <arthurdanjou@outlook.fr>
Date: Wed, 9 Oct 2024 14:46:22 +0200
Subject: [PATCH] Fix

---
 M1/Monte Carlo Methods/Exercise2.rmd |  2 +-
 M1/Monte Carlo Methods/Exercise3.rmd |  2 +-
 M1/Monte Carlo Methods/Exercise6.rmd | 10 +++-------
 3 files changed, 5 insertions(+), 9 deletions(-)

diff --git a/M1/Monte Carlo Methods/Exercise2.rmd b/M1/Monte Carlo Methods/Exercise2.rmd
index 6d27e0d..eb5c2fe 100644
--- a/M1/Monte Carlo Methods/Exercise2.rmd	
+++ b/M1/Monte Carlo Methods/Exercise2.rmd	
@@ -42,5 +42,5 @@ for (j in (1:n)) {
   i <- 1
 }
 hist(S, freq = FALSE)
-# curve(dpois(S, lambda = 4), add = TRUE, col = "red")
+curve(dpois(S, lambda = 4), add = TRUE, col = "red")
 ```
diff --git a/M1/Monte Carlo Methods/Exercise3.rmd b/M1/Monte Carlo Methods/Exercise3.rmd
index f5bb234..c87e9a8 100644
--- a/M1/Monte Carlo Methods/Exercise3.rmd	
+++ b/M1/Monte Carlo Methods/Exercise3.rmd	
@@ -12,6 +12,6 @@ BM <- function(n) {
 n <- 10e4
 X <- BM(n)
 
-hist(X, breaks = 100, freq = FALSE)
+hist(X, breaks = 50, freq = FALSE)
 curve(dnorm(x), add = TRUE, col = "red")
 ```
\ No newline at end of file
diff --git a/M1/Monte Carlo Methods/Exercise6.rmd b/M1/Monte Carlo Methods/Exercise6.rmd
index 5e3990e..a16eff8 100644
--- a/M1/Monte Carlo Methods/Exercise6.rmd	
+++ b/M1/Monte Carlo Methods/Exercise6.rmd	
@@ -2,21 +2,17 @@
 
 ```{r}
 f <- function(x) {
-  return(
-    (2 / pi * sqrt(1 - x^2)) * (x >= -1 & x <= 1)
-  )
+  2 / pi * sqrt(1 - x^2) * (x >= -1 & x <= 1)
 }
 
 n <- 10000
 
 M <- 4 / pi
 g <- function(x) {
-  return(
-    1 / 2 * (x >= -1 & x <= 1)
-  )
+  1 / 2 * (x >= -1 & x <= 1)
 }
 
-x <- NULL
+x <- numeric(0)
 while (length(x) < n) {
   U <- runif(1)
   X <- runif(1, -1, 1)