set.seed(123456) curve(dnorm(x,10,2), xlim = c(4, 16), ylim = c(0.0, 0.22)) par(mfrow=c(2,2)) n1 <- 5 n2 <- 10 n3 <- 20 n4 <- 30 reps <- 10000 ybar5<-numeric(10000) samples_1 <- replicate(reps, rnorm(n1,10,2)) # 5 x 10000 sample matrix ybar5 <- rep(NA, reps) for (i in 1:reps) { ybar5[i] <- mean(samples_1[,i]) } mean(ybar5) var(ybar5) plot(density(ybar5), xlim = c(7, 13), ylim = c(0.0, 1.2)) curve(dnorm(x,10,sqrt(4/n1)), add=T, lty=2) ybar10<-numeric(10000) samples_2 <- replicate(reps, rnorm(n2,10,2)) # 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(7, 13), ylim = c(0.0, 1.2)) curve(dnorm(x,10,sqrt(4/n2)), add=T, lty=2) ybar20<-numeric(10000) samples_3 <- replicate(reps, rnorm(n3,10,2)) # 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(7, 13), ylim = c(0.0, 1.2)) curve(dnorm(x,10,sqrt(4/n3)), add=T, lty=2) ybar30<-numeric(10000) samples_4 <- replicate(reps, rnorm(n4,10,2)) # 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(7, 13), ylim = c(0.0, 1.2)) curve(dnorm(x,10,sqrt(4/n4)), add=T, lty=2) par(mfrow=c(1,1)) plot(density(ybar5), col="black", xlim = c(7, 13), ylim = c(0.0, 1.2)) lines(density(ybar10), col="red", xlim = c(7, 13), ylim = c(0.0, 1.2)) lines(density(ybar20), col="green", xlim = c(7, 13), ylim = c(0.0, 1.2)) lines(density(ybar30), col="blue", xlim = c(7, 13), ylim = c(0.0, 1.2))