From bc58e96fc747981a125cefb1eede70280cebdfc3 Mon Sep 17 00:00:00 2001 From: ae44f8007c63991902a8055ff9736871 Date: Mon, 13 May 2024 11:35:44 +0000 Subject: [PATCH] Update toy_document_en.Rmd --- module2/exo1/toy_document_en.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/module2/exo1/toy_document_en.Rmd b/module2/exo1/toy_document_en.Rmd index b9a24c0..02a6e7c 100644 --- a/module2/exo1/toy_document_en.Rmd +++ b/module2/exo1/toy_document_en.Rmd @@ -29,7 +29,7 @@ theta = pi/2*runif(N) ## Using a surface fraction argument A method that is easier to understand and does not make use of the $\sin$ function is based on the fact that if $X\sim U(0,1)$ and $Y\sim U(0,1)$, then $P[X^2+Y^2\leq 1] = \pi/4$ (see ["Monte Carlo method" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach: - + ```{r} set.seed(42) N = 1000 @@ -40,7 +40,7 @@ ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + t ``` -It is then straightforward to obtain a (not really good) approximation to $\pi$ by counting how many times, on average, $X^2+Y^2$ is smaller than 1: +It is then straightforward to obtain a (not really good) approximation to $\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller than 1: ```{r} 4*mean(df$Accept) -- 2.18.1