From a0e242877ac64a27086a02ede5d9de2439e01ce3 Mon Sep 17 00:00:00 2001
From: Arthur DANJOU <arthurdanjou@outlook.fr>
Date: Wed, 18 Sep 2024 16:53:09 +0200
Subject: [PATCH] Refactor files

---
 M1/Monte Carlo Methods/Exercise1.rmd              |  8 ++++++++
 M1/Monte Carlo Methods/Exercise2.rmd              | 11 +++++++++++
 M1/Monte Carlo Methods/{TP1.Rmd => Exercise3.rmd} | 12 +-----------
 M1/Monte Carlo Methods/Exercise5.rmd              | 12 ++++++++++++
 M1/Monte Carlo Methods/Monte Carlo Methods.Rproj  | 13 -------------
 5 files changed, 32 insertions(+), 24 deletions(-)
 create mode 100644 M1/Monte Carlo Methods/Exercise1.rmd
 create mode 100644 M1/Monte Carlo Methods/Exercise2.rmd
 rename M1/Monte Carlo Methods/{TP1.Rmd => Exercise3.rmd} (63%)
 create mode 100644 M1/Monte Carlo Methods/Exercise5.rmd
 delete mode 100644 M1/Monte Carlo Methods/Monte Carlo Methods.Rproj

diff --git a/M1/Monte Carlo Methods/Exercise1.rmd b/M1/Monte Carlo Methods/Exercise1.rmd
new file mode 100644
index 0000000..589c52d
--- /dev/null
+++ b/M1/Monte Carlo Methods/Exercise1.rmd	
@@ -0,0 +1,8 @@
+# Exercise 1 : Uniform
+
+```{r}
+n <- 10e4
+U <- runif(n)
+X <- 5 * (U <= 0.4) + 6 * (0.4 < U & U <= 0.6) + 7 * (0.6 < U & U <= 0.9) + 8 * (0.9 < U)
+barplot(table(X)/n)
+```
\ No newline at end of file
diff --git a/M1/Monte Carlo Methods/Exercise2.rmd b/M1/Monte Carlo Methods/Exercise2.rmd
new file mode 100644
index 0000000..f3a27d1
--- /dev/null
+++ b/M1/Monte Carlo Methods/Exercise2.rmd	
@@ -0,0 +1,11 @@
+# Exercise 2 : Exponential distribution and related distributions
+
+```{r}
+n <- 10000
+u <- runif(n)
+x <- -1/2 * log(1-u)
+hist(x, breaks = 50, freq = FALSE)
+curve(dexp(x, rate = 2), add = TRUE, col = "red")
+
+qqplot(x, rexp(n, rate = 2))
+```
diff --git a/M1/Monte Carlo Methods/TP1.Rmd b/M1/Monte Carlo Methods/Exercise3.rmd
similarity index 63%
rename from M1/Monte Carlo Methods/TP1.Rmd
rename to M1/Monte Carlo Methods/Exercise3.rmd
index daca898..f5bb234 100644
--- a/M1/Monte Carlo Methods/TP1.Rmd	
+++ b/M1/Monte Carlo Methods/Exercise3.rmd	
@@ -1,12 +1,3 @@
-# Exercise 1 : Uniform
-
-```{r}
-n <- 10e4
-U <- runif(n)
-X <- 5 * (U <= 0.4) + 6 * (0.4 < U & U <= 0.6) + 7 * (0.6 < U & U <= 0.9) + 8 * (0.9 < U)
-barplot(table(X)/n)
-```
-
 # Exercise 3 : Box Muller Algo
 
 ```{r}
@@ -23,5 +14,4 @@ X <- BM(n)
 
 hist(X, breaks = 100, freq = FALSE)
 curve(dnorm(x), add = TRUE, col = "red")
-```
-
+```
\ No newline at end of file
diff --git a/M1/Monte Carlo Methods/Exercise5.rmd b/M1/Monte Carlo Methods/Exercise5.rmd
new file mode 100644
index 0000000..6e7a3fc
--- /dev/null
+++ b/M1/Monte Carlo Methods/Exercise5.rmd	
@@ -0,0 +1,12 @@
+# Exercise 5 : Simulation of Brownian Motion
+
+```{r}
+n <- 1:1100
+brownian <- function (i) {
+  return ((i >= 1 & i <= 100)*(i/100) + (i >= 101 & i <= 110)*(1 + (i - 100)/10) + (i >= 111 & i <= 1110)*(2 + (i - 110)/1000))
+}
+t <- brownian(n)
+W0 <- 0
+Wt <- W0 + sqrt(t) * rnorm(1100)
+plot(t, Wt, type = "o")
+```
\ No newline at end of file
diff --git a/M1/Monte Carlo Methods/Monte Carlo Methods.Rproj b/M1/Monte Carlo Methods/Monte Carlo Methods.Rproj
deleted file mode 100644
index 8e3c2eb..0000000
--- a/M1/Monte Carlo Methods/Monte Carlo Methods.Rproj	
+++ /dev/null
@@ -1,13 +0,0 @@
-Version: 1.0
-
-RestoreWorkspace: Default
-SaveWorkspace: Default
-AlwaysSaveHistory: Default
-
-EnableCodeIndexing: Yes
-UseSpacesForTab: Yes
-NumSpacesForTab: 2
-Encoding: UTF-8
-
-RnwWeave: Sweave
-LaTeX: pdfLaTeX