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M1/Monte Carlo Methods/Monte Carlo Methods.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX

M1/Monte Carlo Methods/TP1-Test.rmd

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+---
+title: "R Notebook"
+output: html_document
+---
+
+The [R plugin](https://www.jetbrains.com/help/pycharm/r-plugin-support.html) for IntelliJ-based IDEs provides
+handy capabilities to work with the [R Markdown](https://www.jetbrains.com/help/pycharm/r-markdown.html) files.
+To [add](https://www.jetbrains.com/help/pycharm/r-markdown.html#add-code-chunk) a new R chunk,
+```{r}
+
+```
+position the caret at any line or the code chunk, then click "+".
+
+The code chunk appears:
+```{r}
+```
+
+Type any R code in the chunk, for example:
+```{r}
+mycars <- within(mtcars, { cyl <- ordered(cyl) })
+mycars
+```
+
+Now, click the **Run** button on the chunk toolbar to [execute](https://www.jetbrains.com/help/pycharm/r-markdown.html#run-r-code) the chunk code. The result should be placed under the chunk.
+Click the **Knit and Open Document** to build and preview an output.

M1/Monte Carlo Methods/TP1.Rmd

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+# Exercice 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)
+```
+
+# Exercice 3 : Box Muller Algo
+
+```{r}
+BM <- function(n) {
+  U1 <- runif(n)
+  U2 <- runif(n)
+  X1 <- sqrt(-2 * log(U1)) * cos(2 * pi * U2)
+  X2 <- sqrt(-2 * log(U1)) * sin(2 * pi * U2)
+  return(c(X1, X2))
+}
+
+n <- 10e4
+X <- BM(n)
+
+hist(X, breaks = 100, freq = FALSE)
+curve(dnorm(x), add = TRUE, col = "red")
+```
+