import numpy as np
#import scipy.stats as stats
import seaborn as sns # seaborn package를 이용
import matplotlib.pyplot as plt # matplotlib.pyplot package를 이용
from numpy import random

# set the random seed:
random.seed(12345)
    
r=1000    

#p.random.seed(12)
z_1 = random.normal(loc=0.0, scale=1.0, size=r)

#np.random.seed(34)
z_2 = random.normal(loc=0.0, scale=1.0, size=r)

#np.random.seed(56)
z_3 = random.normal(loc=0.0, scale=1.0, size=r)

#np.random.seed(78)
z_4 = random.normal(loc=0.0, scale=1.0, size=r)

#np.random.seed(910)
z_5 = random.normal(loc=0.0, scale=1.0, size=r)

chi_5 = z_1**2+z_2**2+z_3**2+z_4**2+z_5**2
mean = np.mean(chi_5)
variance = np.var(chi_5, ddof=1)
print("Mean of chi-distrinution w/ df=5 is :",round(mean,5))
print("Variance of chi-distrinution w/ df=5 is :",round(variance,5))

sns.histplot(data=chi_5, x=None, kde=True).set(title='Histogram of Chi-square w/ df=5')
plt.show()