### Angewandte Stochastik II
### Evgeny Spodarev
### Jürgen Kampf
### Blatt 8

### Aufgabe 2

# Teil c)
X=c(35.1,36.7,33.0,34.5,35.6)
mean(X)
qt(0.975,df=4)
sqrt(var(X))
mean(X)-qt(0.975,df=4)*sqrt(var(X))/sqrt(5)
mean(X)+qt(0.975,df=4)*sqrt(var(X))/sqrt(5)


# Aufgabe 3
# Teil c)

X=array(runif(10^5), dim=c(10^4,10))
M=apply(X,1,mean)
length(M)
# 2,5%-Quantil
quantile(M, p=0.025)
# 97,5%-Quantil
quantile(M, p=0.975)