A shipping company handles containers in three different sizes: (1) 27 ft 3 (3 ×

Question

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:

Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X1 + 125X2 + 512X3.]

a) Expected value

B) Variance

Explanation / Answer

A shipping company handles containers in three different sizes: (1) 27 ft 3 (3 ×

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