PD(d) = 1/9, if d = 1,2,4,5,8

2/9, if d = 0,7

0, otherwise

(A) Let Yn = D1 + D2 + .. . Dn be the sum of n independent samples from PD(d). Calculate An = EY,] and on = \\ Var(Ym ), justifying your answers. (B) Consider the new random variable Z, = (Yn - n) /On. Find E[Z,] and Var(Zn ) justifying your answers. (C) For n in the set = {10, 100, 1000}, generate random variables of digits from Pan (=) (do not display them), plotting the resulting frequencies as bar graphs and compare them to a plot of the function N(z) = Ce-/2 where C is some suitably chosen constant. (D) Explain the results of part (c). (E) If N(z) above is a PDF, calculate the appropriate value of C