3. Define our universe" S as the region in the xy-plane that is described by S = {(2,y) (x+|+ \y -1}. There are an infinite number of solutions to this problem, so I expect to see as many different solutions as there are students in the class. (a) Mathematically and graphically describe three sets. A. , and Ag taken from S that are mutually exclusive but not collectively exhaustive. (b) Mathematically and graphically describe three sets B, B2, and Bs taken from S that are collec- tively exhaustive but not mutually exclusive. (c) Mathematically and graphically describe three sets C, C), and Cg that form an event space for S. Make the area of C, equal twice the area of C, and make the area of Cg equal to three times the area of C. (d) Suppose that a point (1,y) is randomly chosen in S such that any point in S is equally likely to be chosen. Write a MATLAB program (m-file) that simulates and plots 1000 such random points (1,). How many points fall into each of G, C, and Cy? Do these numbers make sense? To set the RNG seed and allow reproducibility of results, use the MATLAB command rng (YourStudent ID) as the first line of your code, and use the rand command to help choose both randy. To improve graph clarity, shade region C dark gray and region G, light gray before plotting your 1000 points This can be done using the patch command