# -*- coding: utf-8 -*-
"""
Created on Mon Jan  3 09:49:09 2022

@author: Sim
"""
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as st

lam = 10
x = np.random.poisson(lam, size=1000)
print(np.mean(x))
print(np.var(x, ddof=1))

mx = list()
for i in range(1000):
    x = np.random.poisson(lam, size=1000)
    mx = np.append(mx, np.mean(x))
print(np.mean(mx))

se = np.sqrt(lam/1000)
x2 = np.linspace(lam-3*se, lam+3*se, 100)
pdf = st.norm.pdf(x2, loc=10, scale=se)

plt.hist(mx, density=True, edgecolor='white' )
plt.plot(x2, pdf, 'r-')