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A shipping company handles containers in three different sizes: (1) 27 ft 3 (3 3 3), (2) 125 ft 3 , and (3) 512 ft

A shipping 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 i = E(Xi) and i2 = V(Xi), suppose that the mean values and standard deviations are as follows:

1 = 230 2 = 260 3 = 140
1 = 11 2 = 12 3 = 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.]

expected value(ft^3):
variance(ft^6):

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