Write down your Student number and the digit probability mass function PD ((1) that you calculated in the first assignment. Include your calculated values of up and Var(D). (A) Let Y,. = D1 + D2 + . .. D,l be the sum of n independent samples from PD(d). Calculate y" = E[Y,,] and a}, = '/Var(Y,,) . justifying your answers. (B) Consider the new random variable Z,l = (Y,, y") la". Find E[Z,,] and Val-(2,.) justifying your answers. (C) For n in the set 6' = {10, 100, 1000}. generate random variables of digits from P2,. (2) (do not display them). plotting the resulting frequencies as bar graphs and compare them to a plot of the function N (z) = Ce'zz'2 where C is some suitably chosen constant. (D) Explain the results of part (c). (E) If N (2) above is a PDF. calculate the appropriate value of C. Pom -= s- H 3-. \"ll-1'69\"! '2' ; 8-. 0 0 dh-l-H $