##   1) 1 is near the median value for the F-distribution

  qf(0.5, 4,10)
  c(1/qf(0.5, 4,10),   qf(0.5, 10,4))
  qf(0.5, 10, 10)

  c(1/qf(0.1, 4,10), qf(0.9, 10,4) ) 

##  2) T^2(df) = F(1, df) 

  n <- 5000    # simulated sample size 
  ddf <- 5
  samp <- rt(n, df = ddf) 
  samp2 <- pmin(samp^2, 10)   

  hist(samp2, breaks = seq(0,10,0.5), freq = FALSE)
   
   ff <- function(x){
        df(x, 1, ddf)
   }
   
  curve(ff, col="red", add = TRUE)