1. find a procedure for sampling uniformly on the surface of the sphere. a. use computer to generate a thousand points that are random, independent, and uniform on the unit sphere, and print the resulting picture. b. by putting sufficiently many independent uniform points on the surface of the earth (not literally but using a computer model, of course), estimate the areas of antarctica and africa, compare your results with the actual values, and make a few comments (e.g., are the relative errors similar? would you expect them to be similar? if not, which one should be bigger? etc.)