#taelle spredninger for normalfordeling #EX=0, sd=1 pnorm(0-2*1,mean=0,sd=1)#P(X <= -2) pnorm(0-1.96*1,mean=0,sd=1)#P(X<= -1.96) 2*pnorm(0-3*2.5,mean=0,sd=2.5) #normalfordeling med middelvaerdi 2 og varians 2.5 #2 slags intervaller Xsample=rnorm(100,mean=2,sd=sqrt(2.5)) Xsample mean(Xsample) var(Xsample) plot(Xsample) abline(c(2-2*sqrt(2.5),0),col="blue") abline(c(2+2*sqrt(2.5),0),col="blue") x=c(1:100) plot(x,rep(2,100),ylim=c(2-4*sqrt(2.5),2+4*sqrt(2.5)),type="l") for (i in 1:100) segments(x[i],Xsample[i]-2*sqrt(2.5),x[i],Xsample[i]+2*sqrt(2.5),col="blue") ######################## #CLT xunif=runif(1000)#generate random uniform numbers between 0 and 1 round(xunif,2) hist(xunif) mean(xunif) var(xunif) hist(xunif) dev.copy2eps(file="unif_hist.eps")#dev.copy2pdf produces .pdf figures nsim=1000 nexp=1000 xbar=rep(0,nexp) for (i in 1:nexp){ x=runif(nsim) xbar[i]=mean(x) } hist(xbar,probability=T) dev.copy2eps(file="unifxbarhist.eps") #binary nsim=1000 nexp=1000 xbar=rep(0,nexp) for (i in 1:nexp){ #=runif(nsim) x=runif(nsim)<0.2 xbar[i]=mean(x) } hist(xbar,probability=T) m=c(1:6) probs=c(1/8,1/8,1/8,1/8,1/4,1/4) sum((m-1/8)^2*probs) hist(rgamma(1000,shape=0.5,scale=0.001)) hist(runif(1000)) nsim=1000 nexp=10000 xbar=rep(0,nexp) for (i in 1:nexp){ #=runif(nsim) x=rgamma(nsim,shape=0.5,scale=0.001) xbar[i]=mean(x) } hist(xbar,probability=T) #binary nsim=1000 nexp=10000 xbar=rep(0,nexp) for (i in 1:nexp){ #=runif(nsim) x=runif(nsim)<0.2 xbar[i]=mean(x) } hist(xbar,probability=T)