Data Science Python 3.0 Problem:

In [5]: import numpy as np import matplotlib.pylab as plt import pandas as pd matplotlib inline [35 points] Problem 1 Monte Carlo Estimation of Definite Integrals One really cool application of random variables is using them to approximate integrals/area under a curve. This method of approximating integrals is used constantly in computational science to approximate really difficult integrals that we never want to do by hand. In this exercise you'll figure out how we can do this in practice and test your method on a very simple integral. Part A Compute by-hand, the integral f(x) = sin(x) for 0 x In [5]: import numpy as np import matplotlib.pylab as plt import pandas as pd matplotlib inline [35 points] Problem 1 Monte Carlo Estimation of Definite Integrals One really cool application of random variables is using them to approximate integrals/area under a curve. This method of approximating integrals is used constantly in computational science to approximate really difficult integrals that we never want to do by hand. In this exercise you'll figure out how we can do this in practice and test your method on a very simple integral. Part A Compute by-hand, the integral f(x) = sin(x) for 0 x