A shipping company handles containers in three different sizes: (1) 27 ft3 (3 × 3 × 3), (2) 125 ft³, and (3) 512 ft³. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given...

Extracted text: A shipping company handles containers in three different sizes: (1) 27 ft3 (3 × 3 × 3), (2) 125 ft³, and (3) 512 ft³. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With p; = E(X;) and of V(X;), suppose that the mean values and standard deviations are as follows: H1 = 230 M2 = 260 Из = 110 01 = 11 02 = 13 03 = 6 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = expected value ft3 27X1 + 125X2 + 512X3.] variance ft6