set.seed(123456) curve(dunif(x,min=0, max=1)) par(mfrow=c(2,2)) n1 <- 2 n2 <- 10 n3 <- 20 n4 <- 30 reps <- 10000 ybar2<-numeric(10000) samples_1 <- replicate(reps, runif(n1,min=0, max=1)) # 2 x 10000 sample matrix ybar2 <- rep(NA, reps) for (i in 1:reps) { ybar2[i] <- mean(samples_1[,i]) } mean(ybar2) var(ybar2) plot(density(ybar2), xlim = c(0, 1), ylim = c(0,8)) curve(dnorm(x,0.5,sqrt((1/12)/n1)), add=T, lty=2) ybar10<-numeric(10000) samples_2 <- replicate(reps, runif(n2,min=0, max=1)) # 10 x 10000 sample matrix ybar10 <- rep(NA, reps) for (i in 1:reps) { ybar10[i] <- mean(samples_2[,i]) } mean(ybar10) var(ybar10) plot(density(ybar10),xlim = c(0, 1), ylim = c(0,8)) curve(dnorm(x,0.5,sqrt((1/12)/n2)), add=T, lty=2) ybar20<-numeric(10000) samples_3 <- replicate(reps, runif(n3,min=0, max=1)) # 20 x 10000 sample matrix ybar20 <- rep(NA, reps) for (i in 1:reps) { ybar20[i] <- mean(samples_3[,i]) } mean(ybar20) var(ybar20) plot(density(ybar20),xlim = c(0, 1), ylim = c(0, 8)) curve(dnorm(x,0.5,sqrt((1/12)/n3)), add=T, lty=2) ybar30<-numeric(10000) samples_4 <- replicate(reps, runif(n4,min=0, max=1)) # 30 x 10000 sample matrix ybar30 <- rep(NA, reps) for (i in 1:reps) { ybar30[i] <- mean(samples_4[,i]) } mean(ybar30) var(ybar30) plot(density(ybar30),xlim = c(0, 1), ylim = c(0, 8)) curve(dnorm(x,0.5,sqrt((1/12)/n4)), add=T, lty=2)