TP 1 Exercice 2

Question 1 on a calculé µ , la moyenne et segma²

pop=seq(10,100,10)
pop

##  [1]  10  20  30  40  50  60  70  80  90 100

N=10
mu=mean(pop)
mu

## [1] 55

sigma2= ((N-1)/N)*var(pop)
sigma2

## [1] 825

Question2 a/b/c/ réalisation d’ un tirage aléatoire simple sans remise a proba nulle on a calculer la moyenne y_bar estimé variance de y_bar estimé variance estimé de y_bar estimé

TIRAGE_SIMPLE_ALEATOIRE=function(pop) {
  n=3
  N=100
  ech=sample(x = pop ,size = n,replace = TRUE ,prob=NULL)  
  y_bar_pear=mean(ech)
  var_pear= sigma2 /n
  s2c=var(ech)    
  var_estim_y_bar_pear=s2c/n   
  v=c(ech,y_bar_pear,var_pear,var_estim_y_bar_pear)
  return(v)
}

Question 2 d/ on a constuire un intervalle de confiance de niveau 0.95 pour µ

res=replicate(5,TIRAGE_SIMPLE_ALEATOIRE(pop))
  res

##          [,1]     [,2]      [,3]      [,4]      [,5]
## [1,]  90.0000  90.0000 100.00000  30.00000  90.00000
## [2,]  80.0000  10.0000 100.00000  30.00000  40.00000
## [3,]  40.0000  50.0000  50.00000 100.00000  70.00000
## [4,]  70.0000  50.0000  83.33333  53.33333  66.66667
## [5,] 275.0000 275.0000 275.00000 275.00000 275.00000
## [6,] 233.3333 533.3333 277.77778 544.44444 211.11111

Question 3 la representation de 5 intervalles de confiance

ICinf=1:5
  ICsup=1:5
  
  for(i in 1:5){
    ICinf[i]=res[4,i]-(1.96*sqrt(res [6,i]))
    ICsup[i]=res[4,i]+(1.96*sqrt(res [6,i]))
  }
  
       plot(1:5,ICinf,type = "o" ,ylim=c(min(min(ICinf),min(ICsup)),max(max(ICinf),max(ICsup))))
             par(new=T)
       plot(1:5,ICsup,type = "o" ,ylim=c(min(min(ICinf),min(ICsup)),max(max(ICinf),max(ICsup))))
      abline(mu,0)