#!/usr/bin/env python
# coding: utf-8

# # Week 12: Estimation
# 
# 
# 
#  #### [Back to main page](https://petrosyan.page/fall2020math3215)
# 

# In[6]:


# nbi:hide_in
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams["figure.figsize"] = (10, 5)

n=100 #number of samples
# intsize the number of class intervals
class_num = 20

mean = 2
sigma = 3

mean0 = 0
sigma0 = 1

 
data = np.random.randn(n) * sigma + mean

MLEmean = np.mean(data)
MLEvar = np.var(data)

tau2 = 1/(1/sigma0**2 + n/sigma**2)
Bmean = tau2 * ((1/sigma0**2) * mean0 + (n/sigma**2) * MLEmean)






# In[7]:


MLEmean


# In[8]:


MLEvar


# In[ ]:


# nbi:hide_in
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams["figure.figsize"] = (10, 5)

n=100 #number of samples
# intsize the number of class intervals
class_num = 20

mean = 2
sigma = 3

mean0 = 0
sigma0 = 1

 
data = np.random.randn(n) * sigma + mean

MLEmean = np.mean(data)
MLEvar = np.var(data)

tau2 = 1/(1/sigma0**2 + n/sigma**2)
Bmean = tau2 * ((1/sigma0**2) * mean0 + (n/sigma**2) * MLEmean)