This exercise concerns Polya's urn and has a computing/simulation component. Let us start with one red and one green ball as in the lecture and let Mn be the fraction of red balls at the nth stage. 1. Show that the distribution of Mn is uniform on the set 1 2 n+1 n+2,n+2,...,n+2 . (Use mathematical induction, that is, note that it is obviously true for n = 0 and show that if it is true for n then it is true for n+1.) 2. Write a short program that will simulate this urn. Each time you run the program note the fraction of red balls after 2000 draws and after 4000 draws. Compare the two fractions. Then, repeat this thirty times