import numpy as np
import scipy.stats as stats
import seaborn as sns
import matplotlib.pyplot as plt

# set the random seed:
np.random.seed(12345)

# set sample size:
n=2

# initialize sampling dist. to an array of length r=10000 to later store results:
r = 10000
sample_dist = np.empty(r)

# repeat r times:
for j in range(1,r):
    # draw a sample and store the sample mean in pos. j=0,1,... of sample_dist:
    sample = stats.norm.rvs(2.5, 1.118, size=2)
    sample_dist[j] = np.var(sample, ddof=1)

mean = np.mean(sample_dist)
variance = np.var(sample_dist,ddof=1)

print("Mean of sample variance distribution is :", mean)
print("Variance of sample variance distribution is :", variance)

fig, ax = plt.subplots()

sns.histplot(data=sample_dist, ax=ax, kde=True).set(title='Histogram of Sampling_dist')
ax.set_xlim(0,10)