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:

r=1000    

np.random.seed(1)
z = random.normal(loc=0.0, scale=1.0, size=r)

np.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

sqchi_5 = np.sqrt(chi_5/5)

t_5 = z / sqchi_5

sns.histplot(data=t_5, x=None, kde=True).set(title='Histogram of Student-t w/ df=5')
plt.show()