Simulation of Renewal Process.R

size<-1000
devider<-10
Nt<-numeric(size)
result<-numeric(size/devider)
for (i in 1:size) {
  X<-runif(1000, min=0, max=1)
  S<-cumsum(X)
  t<-100
  Nt[i]<-sum(S<t)
    result[i]<-sum(Nt)/i
}
mean(Nt)
exp(.5)-1
plot(y=result, x=1:size/devider,pch=16,cex=0.1)
abline(h=exp(t)-1, col='red',lwd=2)
hist(Nt, probability = T)
somevalue<-seq(from=150,to=250,by=.1)

sd<-sqrt(t*1/(12*.5^3))

lines(x=somevalue,y = dnorm(somevalue, mean=t/.5, sd = sd))
#plot(table(Nt))


exp<-rnorm(100000, mean=0, sd=1)
hist(exp)