diff --git a/module2/exo1/toy_document_fr.Rmd b/module2/exo1/toy_document_fr.Rmd index f965d1752265c3355917fe69d3e058c908a6e978..6abff9526ad29fbc95da472555da3e8d37639a45 100644 --- a/module2/exo1/toy_document_fr.Rmd +++ b/module2/exo1/toy_document_fr.Rmd @@ -26,8 +26,7 @@ theta = pi/2*runif(N) 2/(mean(x+sin(theta)>1)) ``` -## Using Fraction arguement - +## Using Fraction arguement A method that is easier to understand and does not make use of the sin function is based on the fact that if $X\sim U(0,1)$ et $Y\sim U(0,1)$ then $P[X^2+Y^2\leq 1] = \pi/4$ [Mont carlo method](https://en.wikipedia.org/wiki/Monte_Carlo_method). The following code uses this approach: ```{r} @@ -39,8 +38,7 @@ library(ggplot2) ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw() ``` -It is therefore straightforward to obtain a (not really good) approximation to π by counting how many times, on average, X2+Y2 is smaller than 1 : - +It is therefore straightforward to obtain a (not really good) approximation to π by counting how many times, on average, $X^2 + Y^2$ is smaller than 1 : ```{r} 4*mean(df$Accept)