set.seed(12345) n<-10000; par(mfrow=c(1,2)) 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) z6<-rnorm(n,0,1) z7<-rnorm(n,0,1) z8<-rnorm(n,0,1) z9<-rnorm(n,0,1) z10<-rnorm(n,0,1) chi15<-z1^2+z2^2+z3^2+z4^2+z5^2 chi25<-z6^2+z7^2+z8^2+z9^2+z10^2 f55<-(chi15/5)/(chi25/5) hist(f55, freq=F,xlab="", xlim=c(0, 40),breaks=100) par(new=T) plot(density(f55), axes=F, main="", xlim=c(0, 40), lwd=2, col="blue") curve(df(x, 5, 5), col="black", xlim=c(0, 40), ylim=c(0, 0.55), xlab="f", ylab="f(f)")