# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.expon.html#scipy.stats.expon

import scipy.stats as st
import matplotlib.pyplot as plt
from numpy import linspace 
from math import sqrt,exp,log,floor

REP=10000
mu=10

rv=lambda: st.expon.rvs(scale=mu)

s=0.0
for _ in range(REP):
  r=rv()
#  print(r)
  s+=1+floor(r)

print(s/REP)
print(1.0/(1.0-exp(-1.0/mu)))
print(exp(-1.0/mu))