Use number 500899646 therefore PD(d) is as follows:

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