pBin<-function(k,p,n)
{
newton<-factorial(n)/(factorial(k)*factorial(n-k))
return (newton*p^(k)*(1-p)^(n-k));


}


#rozkład bernoulliego

drawBinomial<-function(p,n)
{

arg<-0:n;
val<-pBin(arg,p,n);
valN<-dnorm(arg,mean=n*p,sd=sqrt(n*p*(1-p)));
plot(arg,val,lwd=3,col="blue",ylim=c(0,max(val,valN)),lty=1,xlab="Liczba sukcesów",ylab="Prawdopodobieństwo");
lines(arg,val,col="blue");

lines(col="red",arg,valN);
lines(col="red",arg,valN,type="p");
legend("topright", c("N", "Bin"), lty=c(1,1),col = c("blue","red"), pch = c(1, 1) )
}


drawDist<-function(p,n)
{

arg<-0:n;
val<-cumsum(pBin(arg,p,n));
plot(arg,val,lwd=3,col="blue",lty=1,xlab="Liczba sukcesów",ylab="Prawdopodobieństwo");
lines(arg,val,col="blue");
valN<-pnorm(arg+0.5,mean=n*p,sd=sqrt(n*p*(1-p)));
lines(col="red",arg,valN);
lines(col="red",arg,valN,type="p");
legend("bottomright", c("N", "Bin"), lty=c(1,1),col = c("blue","red"), pch = c(1, 1) )
}




draw<-function(p,n)
{

par(mfrow=c(2,1))
drawBinomial(p,n);
drawDist(p,n);


}


draw(0.5,10);