A shipping company handles containers in three different sizes: (1) 27 ft3 (3 x

Question

A shipping company handles containers in three different sizes: (1) 27 ft3 (3 x 3 x 3), (2) 125 ft3, and (3) 512 ft3. Let X 1, 2, 3) denote the number of type i containers shipped during a given week. With = E(Xi) and ,2-V(X), suppose that the mean values and standard deviations are as follows: M1=210 2 = 250 3= 140 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 variance ft 3 ft 6 (b) Would your calculations necessarily be correct if the Xs were not independent? Explain. The expected value would be correct, but the variance would not be correct. Neither the expected value nor the variance would be correct. The expected value would not be correct, but the variance would be correct. Both the expected value and the variance would be correct.

Explanation / Answer

a) Expected value = E(27X1 + 125X2 + 512X3) = 27*210 + 125*250 + 512*140 = 108600

Variance = V(27X1 + 125X2 + 512X3) = 272 *102 + 1252 * 122 + 5122 * 82 = 19100116

b) Option A is correct.

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