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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 µi = E(Xi) and σi2 = V(Xi), suppose that the
- a. Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X1 + 125X2 + 512X3.]
- b. Would your calculations necessarily be correct if the Xi’s were not independent? Explain.
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Chapter 5 Solutions
Probability and Statistics for Engineering and the Sciences
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