set.seed(12345)

n<-10000;

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, breaks=100)