# -*- coding: utf-8 -*-
"""
Created on Sun Jan 12 17:09:04 2025

@author: arnau
"""

import numpy as np
import numpy.random as rd
import matplotlib.pyplot as plt

def exp(lambda_):
    return -1/lambda_*np.log(1-rd.rand())




T = np.linspace(0, 20,100)
F = np.zeros(len(T))

N = 1000
lambda_ = 1

for _ in range (N):
    for i in range(len(T)):
        if exp(lambda_)<= T[i]:
            F[i]+=1/N

plt.plot(T,F)
plt.plot(T, 1-np.exp(-lambda_*T),'r:')