Refactor files

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)
+```

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))
+```

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")
-```
-
+```

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")
+```

M1/Monte Carlo Methods/Monte Carlo Methods.Rproj

@@ -1,13 +0,0 @@
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