diff --git a/M1/Monte Carlo Methods/Exercise2.rmd b/M1/Monte Carlo Methods/Exercise2.rmd index 29f1ece..eec71d6 100644 --- a/M1/Monte Carlo Methods/Exercise2.rmd +++ b/M1/Monte Carlo Methods/Exercise2.rmd @@ -16,12 +16,32 @@ qqplot(x, rexp(n, rate = 2)) ```{r} lambda <- 1.5 n <- 10000 +d <- 10 S <- numeric(n) for (i in 1:n) { - u <- runif(10) + u <- runif(d) x <- -1/lambda * log(1-u) S[i] <- sum(x) } hist(S, freq = FALSE, breaks = 50) -curve(dgamma(x, shape = 10, rate = lambda), add = TRUE, col = "red") +curve(dgamma(x, shape = d, rate = lambda), add = TRUE, col = "red") +``` + +### Question 3 +```{r} +lambda <- 4 +n <- 10000 +X <- numeric(n) +p <- 1 +for (i in 1:n) { + S <- -1/lambda * log(1-runif(1)) + while (S <= 1) { + S <- x - 1/lambda * log(1-runif(1)) + p <- p+1 + } + X[i] <- p + p <- 1 +} +hist(X, freq = FALSE, breaks = 50) +curve(dpois(x, lambda), add = TRUE, col = "red") ```