set.seed(123456) curve(dchisq(x,1)) par(mfrow=c(2,2)) n1 <- 2 n2 <- 10 n3 <- 20 n4 <- 30 reps <- 10000 ybar2<-numeric(10000) samples_1 <- replicate(reps, rchisq(n1,1)) # 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, 10), ylim = c(0.0, 1.6)) curve(dnorm(x,1,sqrt(1.0)), add=T, lty=2) ybar10<-numeric(10000) samples_2 <- replicate(reps, rchisq(n2,1)) # 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, 4), ylim = c(0.0, 1.6)) curve(dnorm(x,1,sqrt(0.2)), add=T, lty=2) ybar20<-numeric(10000) samples_3 <- replicate(reps, rchisq(n3,1)) # 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, 3), ylim = c(0.0, 1.6)) curve(dnorm(x,1,sqrt(0.1)), add=T, lty=2) ybar30<-numeric(10000) samples_4 <- replicate(reps, rchisq(n4,1)) # 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(0.3, 1.7), ylim = c(0.0, 1.6)) curve(dnorm(x,1,sqrt(0.0667)), add=T, lty=2)