The value of may be approximated by Monte Carlo methods. Consider the region of the xy-plane bounded by 0 x 1 and 0 y 1. By selecting a large number of random points within this region and counting the proportion of them lying beneath the function y =

1 x2 describing a quarter-circle, one can estimate /4, this being the area bounded by the axes and y(x). Write a program to estimate the value of by this method. Hint: use Pythons random module. The method random.random() generates a (pseudo-)random number between 0. and 1. See Section 4.5.1 for more information.