QUESTION 1:

QUESTION 2:

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#All packages needed import numpy as np import scipy.special as spsp import scipy.stats as spspt import matplotlib.pyplot as plt &matplotlib inline study the Monte-Carlo integration problem based on the following integration: xp 1 + T S = Compute the integration problem above using Monte-Carlo Integral based on 1000 samples. Construct the corresponding 95% confidence interval for the true value of the integration. [] This integration problem has an analytical solution equals z. Repeat Q1 500 times will allow us to collect 500 different Monte-Carlo integration results. Also, we will get 500 different 95% confidence intervals. Plot the distribution of 500 integration results you get. Comment on the shape of the distribution and argue why you see this shape. For this plot, use bins=20. Compute the percentage of times these confidence intervals contain the analytical solution. [] #All packages needed import numpy as np import scipy.special as spsp import scipy.stats as spspt import matplotlib.pyplot as plt &matplotlib inline study the Monte-Carlo integration problem based on the following integration: xp 1 + T S = Compute the integration problem above using Monte-Carlo Integral based on 1000 samples. Construct the corresponding 95% confidence interval for the true value of the integration. [] This integration problem has an analytical solution equals z. Repeat Q1 500 times will allow us to collect 500 different Monte-Carlo integration results. Also, we will get 500 different 95% confidence intervals. Plot the distribution of 500 integration results you get. Comment on the shape of the distribution and argue why you see this shape. For this plot, use bins=20. Compute the percentage of times these confidence intervals contain the analytical solution. []