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(123456)

# set sample size:
n1=2
n2=5
n3=10
n4=30

# initialize sampling dist. to an array of length r=10000 to later store results:
r = 10000
sample_dist_2 = np.empty(r)
sample_dist_5 = np.empty(r)
sample_dist_10 = np.empty(r)
sample_dist_30 = 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_2 = stats.norm.rvs(2.5, 1.1182, size=n1)
    sample_dist_2[j] = np.mean(sample_2)

# 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_5 = stats.norm.rvs(2.5, 1.1182, size=n2)
    sample_dist_5[j] = np.mean(sample_5)

# 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_10 = stats.norm.rvs(2.5, 1.1182, size=n3)
    sample_dist_10[j] = np.mean(sample_10)
    
# 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_30 = stats.norm.rvs(2.5, 1.1182, size=n4)
    sample_dist_30[j] = np.mean(sample_30)    

mean_2 = np.mean(sample_dist_2)
variance_2 = np.var(sample_dist_2)
print("Mean of sampling distribution w/ n=2 is :", mean_2)
print("Variance of sampling distribution w/ n=2 is :", variance_2)

mean_5 = np.mean(sample_dist_5)
variance_5 = np.var(sample_dist_5)
print("Mean of sampling distribution w/ n=5 is :", mean_5)
print("Variance of sampling distribution w/ n=5 is :", variance_5)

mean_10 = np.mean(sample_dist_10)
variance_10 = np.var(sample_dist_10)
print("Mean of sampling distribution w/ n=10 is :", mean_10)
print("Variance of sampling distribution w/ n=10 is :", variance_10)

mean_30 = np.mean(sample_dist_30)
variance_30 = np.var(sample_dist_30)
print("Mean of sampling distribution w/ n=30 is :", mean_30)
print("Variance of sampling distribution w/ n=30 is :", variance_30)

fig, ax = plt.subplots()
sns.histplot(data=sample_dist_2, x=None, kde=True).set(title='Histogram of Sampling_dist_2')
ax.set_xlim(-1,6)
plt.show()

fig, ax = plt.subplots()
sns.histplot(data=sample_dist_5, x=None, kde=True).set(title='Histogram of Sampling_dist_5')
ax.set_xlim(-1,6)
plt.show()

fig, ax = plt.subplots()
sns.histplot(data=sample_dist_10, x=None, kde=True).set(title='Histogram of Sampling_dist_10')
ax.set_xlim(-1,6)
plt.show()

fig, ax = plt.subplots()
sns.histplot(data=sample_dist_30, x=None, kde=True).set(title='Histogram of Sampling_dist_30')
ax.set_xlim(-1,6)
plt.show()

fig = plt.figure(figsize=(14,7))
# 두 개의 그래프를 한 페이지에 그림
fig, axs = plt.subplots(ncols=2)
fig, ays = plt.subplots(ncols=2)

sns.histplot(data=sample_dist_2, x=None, ax=axs[0]).set(title='Histogram of Sample_dist_2 & 5')
sns.histplot(data=sample_dist_5, x=None, ax=axs[1])
fig.subplots_adjust(wspace=0.5) # 우측그림의 좌우 간격을 조정
#plt.savefig('C:/BOOK/PyBasics/PyStat/code/sample_dist-1.png')

sns.histplot(data=sample_dist_10, x=None, ax=ays[0]).set(title='Histogram of Sample_dist_10 & 30')
sns.histplot(data=sample_dist_30, x=None, ax=ays[1])
fig.subplots_adjust(wspace=0.5) # 우측그림의 좌우 간격을 조정
#plt.savefig('C:/BOOK/PyBasics/PyStat/code/sample_dist-2.png')