f=function(x){2*x}                   # * is multiplication, \ is division
x=seq(0,1,0.1); y=f(x)               # makes grid 0.0, 0.1, ..., 0.9, 1.0 
Finv=function(p){sqrt(p)}            # sqrt is square root
simulated.data=Finv(runif(100000))   # 100000 random draws from f(x)=2*x
hist(simulated.data,freq=F)          # make a histogram, freq=F makes it integrate to one
lines(x,y)                           # superimpose the TRUE (usually unknown) density on top
mean(simulated.data)                 # estimate mean through simulation
sd(simulated.data)                   # estimate standard deviation
quantile(simulated.data,0.25)        # estimate Q1, i.e. x_0.25 from simulation
quantile(simulated.data,0.75)        # estimate Q3
Finv(0.25)                           # TRUE x_0.25
Finv(0.75)                           # TRUE x_0.75