rm(list = ls())
set.seed(2026)

# Une seule loi uniforme

n = 150000
U = runif(n, min = 0, max = 1)
h = 4*sqrt(1-U^2)
pi_1 = mean(h)
var_1 = var(h)
pi_1
var_1

# Deux lois uniformes

X = runif(n, min = 0, max = 1)
Y = runif(n, min = 0, max = 1)

h = 4*((X^2 + Y^2)<=1)
pi_2 = mean(h)
var_2 = var(h)
pi_2
var_2