1d:T7ee,# Buffon Simulations of the experiment of Buffon. ```r Buffon(p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500)) ``` ## Arguments - `p`: Probability of occurrence of some event. - `width`: Width of the band where the probabilities are represented. - `r`: Array of four values, representing the numbers of repetitions of the experiment that will be carried out. ## Returns Four graphics, each one is the simulation of the experiment of Buffon for the number of repetitions contained in the array r. ## References Gnedenko, B. V. (1978). The Theory of Probability. Mir Publishers. Moscow. ## Author(s) Larisa Zamora and Jorge Diaz ## Note Department of Mathematics. University of Oriente. Cuba. ## Examples ```r Buffon(p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500)) ## The function is currently defined as function (p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500)) { Position <- function(k, colum) { PE <- k%/%colum Resto <- k%%colum if (Resto == 0) { fila <- PE columna <- colum } else { fila <- PE + 1 columna <- Resto } Position <- list(fila, columna) return(Position) } nf <- layout(matrix(c(1, 2, 3, 4), 2, 2, byrow = TRUE), TRUE) k <- 0 la <- p - width lb <- p + width if (la < 0) la <- 0 if (lb > 1) lb <- 1 for (j in 1:4) { k <- k + 1 Probcara <- array(0, dim = r[j]) for (i in 1:r[j]) { binomial <- rbinom(i, 1, p) cara <- length(binomial[binomial == 1]) Probcara[i] <- cara/i } P <- Position(k, 2) fila <- P[[1]] colum <- P[[2]] mfg <- c(fila, colum, 2, 2) a <- as.character(r[j]) plot(Probcara, type = "p", main = paste0("n=", a), xlab = "Repetitions", ylab = "Probability", font.main = 3, col = "blue", ylim = c(la, lb)) abline(h = p, col = "red", lty = 1, lwd = 2) } } ```

Buffon function