Consider a hypercube of edge length l = 2 centered at the origin, i.e., [1, 1]d. In this question, you shall uses Monte Carlo simulation to estimate probabilities. Monte Carlo means drawing random points and using their frequencies to approximate probabilities. To carry out the experiment, you will need to write a python script to do the following: For each dimension d = 1, . . . , 100, generate n = 10,000 points uniformly at random in [1, 1]d. Then carry out the following tasks. 1. Estimate the fraction of sampled points lying inside the largest hypersphere that can be inscribed inside the hypercube. Plot the fraction versus d and report the smallest d at which it is essentially zero (e.g., 104). 2. Let = 0.01. Define the thin shell as [1, 1]d \ [(1 ), 1 ]d ((i.e., the difference between the outer hypercube and inner hypercube, or the thin shell along the boundaries)). Estimate the fraction of sampled points in this shell as a function of d. Plot the fraction versus d. Find the smallest d 2000 for which the fraction is at least 0.9999. Use binary search or coarse stepping (e.g