A shipping company handles containers in three different sizes: (1) 27 ft3 (3 Ý 3 Ý 3), (2) 125 ft3, and (3) 512 ft3. Let Xi (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With?1 = 230 ?2 = 240 ?3 = 120?1 = 11 ?2 = 12 ?3 = 7(a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X1 + 125X2 + 512X3.]expected value ft3variance ft6(b) Would your calculations necessarily be correct if the Xi's were not independent?