set.seed(12345) n<-10000; par(mfrow=c(1,2)) z<-rnorm(n,0,1) z1<-rnorm(n,0,1) z2<-rnorm(n,0,1) z3<-rnorm(n,0,1) z4<-rnorm(n,0,1) z5<-rnorm(n,0,1) chi5<-z1^2+z2^2+z3^2+z4^2+z5^2 sqchi5<-sqrt(chi5/5) t5<-z/sqchi5 hist(t5, freq=F,xlab="", xlim=c(-11, 11),breaks=100) par(new=T) plot(density(t5), axes=F, main="", xlim=c(-11, 11), lwd=2, col="blue") curve(dt(x, 5, ncp=0), col="black", xlim=c(-11, 11), ylim=c(0, 0.39), xlab="t", ylab="f(t)")