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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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