Let X and X' be independent random variables from distribution F. The expected value of the difference of X and X' is called the Gini mean difference (GMD) of X or F, denoted as A. That is, A(F) = A(X) := EX - X'|. (a) Prove that A is a scale parameter, i.e., prove that A(aX + b) = JaJA(X) for nonzero a and any b. (b) If F = N(0, 1), what is the distribution of X - X"? (c) Using the result (b), obtain A(F) where F = N(0, 1). (d) What is the GMD of the normal distribution with a mean / and standard devia- tion o. (Hint: using result of (a) and (c))