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# Techniques de sondage TP1
# Q1
data = read.csv2('data/dep69.csv')
n = 27
N = 275
ech_indexes = sample(1:N, n)
ech = data[ech_indexes,]
est_tot = (275/27) * sum(ech$Pop_totale)
est_moyenne = est_tot / N
est_var = (1-n/N)*var(ech$Pop_totale)/n

vect_est_moyenne = replicate(10000, mean(data[sample(1:275, 27),]$Pop_totale))
vect_est_variance_divided_by_n = replicate(10000, (1-n/N)*var(data[sample(1:275, 27),]$Pop_totale)/n)
vect_est_variance_not_divided_by_n = replicate(10000, (1-n/N)*var(data[sample(1:275, 27),]$Pop_totale))

(true_var - mean(vect_est_variance_not_divided_by_n))/true_var # -0.09
(true_var - mean(vect_est_variance_divided_by_n))/true_var # -0.96