## sftp from blindern: 

## com301 of august 2023
#  kiosk 1.18,
#  sum of uniforms bigger than 1: mean should be e.

sim <- 10^6 
Nsim <- 0*(1:sim)

bigenough <- 20

for (ss in 1:sim)
{
uu <- cumsum(runif(bigenough))
Nsim[ss] <- min((1:bigenough)[uu > 1])
}

print(c(sim,bigenough,mean(Nsim),exp(1)))

print(c(mean(Nsim),exp(1)))

nval <- 2:100
probval <- 1/( nval*factorial(nval-2) )
check1 <- sum(nval*probval) # is e
check2 <- sum((nval-exp(1))^2*probval)
print(c(check1,check2))

hist(Nsim)