#Exercise 3 [18 Points] Setting We would like to study the Monte-Carlo integration problem based on the following integration: 52 ** + adx ##Q1. [8 Points] 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. In [O]: N ##Q2. [10 Points] This integration problem has an analytical solution equals 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. In [O]: #Exercise 3 [18 Points] Setting We would like to study the Monte-Carlo integration problem based on the following integration: 52 ** + adx ##Q1. [8 Points] 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. In [O]: N ##Q2. [10 Points] This integration problem has an analytical solution equals 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. In [O]