# MTT Luennot 18.1006, syksy 2006 # Poissonin jakauma ja binomijakauma # Olkoon E(X)=3 ja X~Binom(n,p); n<-10; p<-3/n #x<-0:n; y<-dbinom(x,n,p); plot(x,y) # tai x<-0:n; y<-dbinom(x,n,p); plot(x,y, type="h") n<-20; p<-3/n x<-0:n; y<-dbinom(x,n,p); plot(x,y, type="h") n<-100; p<-3/n x<-0:n; y<-dbinom(x,n,p); plot(x,y, type="h") n<-500; p<-3/n x<-0:n; y<-dbinom(x,n,p); plot(x,y, type="h") x<-0:n; y<-dpois(x,3); plot(x,y, type="h") sqrt(sum(dbinom(x,n,p)-dpois(x,3)^2)) max(abs(dbinom(x,n,p)-dpois(x,3))) #b) par(mfrow=c(3,3)) x<-0:15; y<-dbinom(x,15,p); plot(x,y, type="h") # annetaan p:lle eri arvot # tai par(mfrow=c(3,3)) for(i in 1:9){ y<-dbinom(x,15,i/10);plot(x,y, type="h")} #(c) par(mfrow=c(2,2)) for(n in c(10, 20, 50, 200)){x<-0:n; y<-dbinom(x,n,0.05); plot(x,y, type="h")} x<-0:200; y<-dbinom(x,n,0.05); plot(x,y, type="h", xlim=c(0,30)) dpois(x,3)