diff --git a/module2/exo1/toy_document_en.Rmd b/module2/exo1/toy_document_en.Rmd index 169a1d8c4576e7d0ddf91271a63125197901c3df..08dc557b2fffeb6cdcd4f17f55b5153597430056 100644 --- a/module2/exo1/toy_document_en.Rmd +++ b/module2/exo1/toy_document_en.Rmd @@ -31,6 +31,7 @@ theta = pi/2*runif(N) 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 df = data.frame(X = runif(N), Y = runif(N)) @@ -42,5 +43,6 @@ 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: ```{r} + 4*mean(df$Accept) ``` \ No newline at end of file