Beispiel 1:

%r
p <- (choose(20,8)*choose(12,4)*choose(8,4))/4^20 
p


n<-10000
y <- numeric(n)  
for(i in 1:n){
  x <- sample(1:4,20,replace=TRUE)  
  y[i] <- 1*(sum(x==1)==8)*(sum(x==2)==4)*(sum(x==3)==4)*(sum(x==4)==4)  
}
mean(y)  
p   
mean(y)-p 




Beispiel 2:


%r
pneu <- 4*(choose(20,8)*choose(12,4)*choose(8,4))/4^20


n<-10000
y <- numeric(n)
for(i in 1:n){
  x <- sample(1:4,20,replace=TRUE)
  y[i] <- 1*(((sum(x==1)==8)&(sum(x==2)==4)&(sum(x==3)==4))
             |((sum(x==1)==4)&(sum(x==2)==8)&(sum(x==3)==4))
             |((sum(x==1)==4)&(sum(x==2)==4)&(sum(x==3)==8))
             |((sum(x==1)==4)&(sum(x==2)==4)&(sum(x==3)==4)))
}
mean(y)
pneu
mean(y)-pneu




Beispiel 3:


%r
au <- 4      
as<- 20     
ub <- 6     
ag <- 0      

for(i1 in 0:ub){                     

  m1 <- choose(as, i1)
  
  for(i2 in 0:ub){                   
    
    m2 <- choose(as-i1, i2)
    
    for(i3 in 0:ub){
      
      m3 <- choose(as-i1-i2, i3)
       
       if (as- i1 - i2 - i3 <=ub){  
        
        ag <- ag + m1*m2*m3 
        }
     }
   }
}
ag   
kug <- au^as 
kug
ag/kug



Beispiel 4:



n <- 10000  
x<- numeric(n)
p1<- 0.3  
p2<- 0.8  
v1 <- 0   
v2 <- 0   
for (i in 0:n ) {   
  v1 <- v1 + dgeom(i,p1)*i 
  v2 <- v2 + dgeom(i,p2)*i 
}
b1 <- (v1 + 1)*100  
b2 <- (v2 + 1)*100  
b1
b2
b1-b2 



Beispiel 5:



pr <- 0.25
pd <- 0.35
pt <- 0.4


pr^5
dbinom(5,5,pr)




s <- 0
for(i in 2:5){
  s <- s + choose(5,i)*pd^i*pt^(5-i)}
s



ps <- pd + pt
pbinom(3,5,ps)