# -*- coding: utf-8 -*-
"""
Created on Fri Feb  6 06:54:43 2026

@author: pjaub
"""

from math import log, exp
import random as rd
import matplotlib.pyplot as plt

plt.close('all')

def simul_exp(a):
    x = rd.random()
    return -1/a*log(x)

N = 1000

lbd = 2

S = [ rd.random() for k in range(N)]
S = [ simul_exp(lbd) for k in range(N)]

x = sorted(S)
y = [(k+1)/N for k in range(N)]
plt.plot(x,y,'k')
a, b = 0 , 5
x = [a + k*(b-a)/N for k in range(N) ]
y = [1 - exp(-lbd*t) for t in x]

plt.plot(x,y,'r')
plt .show()