diff --git a/M1/Monte Carlo Methods/Exercise9.rmd b/M1/Monte Carlo Methods/Exercise9.rmd new file mode 100644 index 0000000..e9b9668 --- /dev/null +++ b/M1/Monte Carlo Methods/Exercise9.rmd @@ -0,0 +1,37 @@ +# Exercise 9 : Estimation of Pi + +## Methode 1 + +```{r} +n <- 150000 + +pi_1 <- function(n) { + U <- runif(n, 0, 1) + return(4 / n * sum(sqrt(1 - U^2))) +} +pi_1(n) +``` + +## Methode 2 +```{r} +n <- 150000 + +pi_2 <- function(n) { + U1 <- runif(n, 0, 1) + U2 <- runif(n, 0, 1) + return(4 / n * sum(U1^2 + U2^2 <= 1)) +} +pi_2(n) +``` + +## Best Estimator +```{r} +n <- 1000 +m <- 150000 + +sample_1 <- replicate(n, pi_1(m)) +sample_2 <- replicate(n, pi_2(m)) + +cat(sprintf("[Methode 1] Mean: %s. Variance: %s \n", mean(sample_1), var(sample_1))) +cat(sprintf("[Methode 2] Mean: %s. Variance: %s", mean(sample_2), var(sample_2))) +```