Add exo 6

M1/Monte Carlo Methods/Exercise6.rmd

@@ -0,0 +1,29 @@
+# Exercise 6 : Rejection - A First Example
+
+```{r}
+f <- function(x) {
+  return(
+    (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)
+  )
+}
+
+x <- NULL
+while (length(x) < n) {
+  U <- runif(1)
+  X <- runif(1, -1, 1)
+  x <- append(x, X[U <= (f(X) / (M * g(X)))])
+}
+
+t <- seq(-1, 1, 0.01)
+hist(x, freq = FALSE, breaks = 50)
+lines(t, f(t), col = "red", lwd = 2)
+```