2. This is a continuation of the previous problem. Recall that X = X+ ... + X7 be the number empty boxes when 10 distinct balls are randomly distributed into 7 distinct boxes. In this question we are interested in finding the variance Var (X) of X. (a) Show that 7 x = (X + ... + X7) = x + [ XiXj. i=1 1si,j7,i#j (b) Argue that E[X] =E[X] for all 1 i 7. (Hint: Compare X; and X?.) (c) Show that for i + j 510 E[XX;] = 710 (d) Finally, using Var(X) =E[X2]-E[X] to find Var(X).