x <- rexp(100, rate = 1)
sum(x)

-------------------------------------

s <- 1:100

for(k in 1:100) {

s[k] <- sum(rexp(100, rate = 1))

}

s
mean(s)
sd(s)
hist(s)
hist(s,20)
qqnorm(s)

z <- (s-mean(s))/sd(s)
hist(z,20)

--------------------------------------

m.hat <- s/100
plot(m.hat)
hist(m.hat,20)

sm<-1:100
for(k in 1:100) {
sm[k] <- sum(rexp(1000, rate = 1))
}
m.hatm <- sm/1000
plot(m.hatm)
hist(m.hatm,20)

hist(m.hat,20)
hist(m.hatm,20)

---------------------------------------

mu.n<-1:1000
x<-rexp(1000, rate = 1)


for(k in 1:1000) {
mu.n[k] <- sum(x[1:k])/k
}
plot(mu.n)

-----------------------------------------------


y.n<-1:1000
x<-rexp(1000, rate = 1)


for(k in 1:1000) {
y.n[k] <- sum(x[1:k])-k
}
plot(y.n)