Crude <- function(n) { X<-runif(n,0,1) mean(1/(1+X)) } antit <- function(n) { X<-runif(n,0,1) mean(1/(1+X)+1/(2-X))/2 } MC.simus <- function(n,Nsim) { MCsimus <- matrix(NA,Nsim,2) for (i in 1:Nsim) { MCsimus[i,1]<-Crude(n) MCsimus[i,2]<-antit(n) } MCsimus } MC<-MC.simus(n=100,Nsim=1000) boxplot(MC[,1],MC[,2], names = c('Crude MC','Antithetic'), ylab = 'estimation of I') eps=0.005; n=100; Nsim=1000 MC<- MC.simus(n,Nsim) proportion<-mean( (abs(MC[,1]-log(2)) <=eps )) proportionA<-mean( (abs(MC[,2]-log(2)) <=eps )) proportion proportionA