Loi normale N(0,1)

Variance connue

Code:

obs1=matrix(rnorm(2000,0,1),ncol=20)
xbar=apply(obs1,1,mean)
Bn=for(i in 1:100){xbar+1.96/sqrt(n)}
An=for(i in 1:100){xbar-1.96/sqrt(n)}
e=Xbar[0>An & 0<Bn]
p=length(e)/100
p



Variance inconnue

Code:

ecarttype=apply(obs1,1,sd)
Bn=for(i in 1:100){xbar+1.96*ecarttype/sqrt(n)}
An=for(i in 1:100){xbar- 1.96*ecarttype/sqrt(n)}
e=Xbar[0>An & 0<Bn]
p=length(e)/100
p


Loi de Student a 2 degres de liberte

Variance connue
impossible

Variance inconnue

Code:

obs2=matrix(rt(2000,2),ncol=20)
xbar=apply(obs2,1,mean)
variance=1.5
qt(0.95,2)
Bn=for(i in 1:100){xbar+1.96*sqrt(variance)/sqrt(n)}
An=for(i in 1:100){xbar-1.96*sqrt(variance)/sqrt(n)}
e=Xbar[0>An & 0<Bn]
p=length(e)/100
p


Loi de Student a 6 degres de liberte

Variance connue

Code:

obs3=matrix(rt(2000,6),ncol=20)
xbar=apply(obs3,1,mean)
variance=1.5
Bn=for(i in 1:100){xbar+1.96*sqrt(variance)/sqrt(n)}
An=for(i in 1:100){xbar-1.96*sqrt(variance)/sqrt(n)}
e=Xbar[0>An & 0<Bn]
p=length(e)/100
p


Variance inconnue

Code:

variance=apply(obs3,1,var)
Bn=for(i in 1:100){xbar+1.96*sqrt(variance)/sqrt(n)}
An=for(i in 1:100){xbar-1.96*sqrt(variance)/sqrt(n)}
e=Xbar[0>An & 0<Bn]
p=length(e)/100
p


Loi du chi-deux a 10 degres de liberte

Variance connue

Code:

obs4=matrix(rchisq(2000, 10, ncp=0),ncol=20)
xbar=apply(obs4,1,mean)
variance=20
Bn=for(i in 1:100){xbar+1.96*sqrt(variance)/sqrt(n)}
An=for(i in 1:100){xbar-1.96*sqrt(variance)/sqrt(n)}
e=Xbar[10>An & 10<Bn]
p=length(e)/100
p

Variance inconnue

Code:

obs4=matrix(rchisq(2000, 10, ncp=0),ncol=20)
xbar=apply(obs4,1,mean)
variance=apply(obs4,1,var)
Bn=for(i in 1:100){xbar+1.96*sqrt(variance)/sqrt(n)}
An=for(i in 1:100){xbar-1.96*sqrt(variance)/sqrt(n)}
e=Xbar[10>An & 10<Bn]
p=length(e)/100
p



Loi de Poisson lambda = 5

Variance connue

Code:

obs5=matrix(rpois(2000, 5),ncol=20)
xbar=apply(obs5,1,mean)
variance=5
Bn=for(i in 1:100){xbar+1.96*sqrt(variance)/sqrt(n)}
An=for(i in 1:100){xbar-1.96*sqrt(variance)/sqrt(n)}
e=Xbar[5>An & 5<Bn]
p=length(e)/100
p