# Script TD 1 - partie 2
#
# Cours de probabilités appliquées Ensimag 1A
# Sujet: https://proba.pages.ensimag.fr/td/td_1_2/



##############
# Exercice 1 #
##############
de6 <- function(n) sample(1:6, n, replace = T)

de6(2)

test_3_theo = sum(1 / (1:6)) / 6
test_3_theo
x = c()
for (i in 1:10000) x <- c(x, sample(1:de6(1), 1, replace = T))
test_3_exp = mean(x == 1)
print(test_3_exp)


##############
# Exercice 3 #
##############
p <- c(0.1, 0.4, 0.2, 0.3)
sum(p) == 1
absc <- cumsum(p)
absc

u <- runif(1)
u

# Méthode 1:
i <- sum(absc > u) + 1
i

# Méthode 2:
borne_sup <- p[1]
i <- 1
while (u > borne_sup) {
  i <- i + 1
  borne_sup <- borne_sup + p[i]
}
i