#   Simulation der Normalverteilung ##
## Methode 1: Inverse Verteilungsfunktion ###
U= runif(10000);
x1 = qnorm(U);
hist(x1);
sum(x1>2);
## Methode 2: Box Muller Transformation
v1= runif(10000); v2= runif(10000);
x2= sqrt(-2*log(v1))*cos(2*pi*v2);
 hist(x2);
sum(x2>2);

### Rejection mit Vergleich zu Exponentialverteilung ###
x3=runif(10000); x3=0*x3;
i=1;
while(i < 10001)
{
x= -log(1-runif(1));
z= runif(1,0,exp(-x));
if (z < dnorm(x)) {x3[i]= x; i=i+1};
}
x3= 2*(runif(10000)<0.5)*x3-x3;
hist(x3)
sum(x3>2);