Ashipping company handles containers in three different sizes: (1) 27 ft3 (3 × 3 × 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 μi = e(xi) and σi2 = v(xi), suppose that the mean values and standard deviations are as follows: μ1 = 200 μ2 = 240 μ3 = 120 σ1 = 10σ2 = 13σ3 = 8 (a) assuming that x1, x2, x3 are independent, calculate the expected value and variance of the total volume shipped. [hint: volume = 27x1 + 125x2 + 512x3.]

assuming that x1, x2, x3 are independent, calculate the expected value and variance of the total volume shipped. [hint: volume = 27x1 + 125x2 + 512x3.]