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

Question

A shipping company handles containers in three different sizes: (1) 27 ft^3 (3 times 3 times 3), (2) 125 ft^3, and (3) 512 ft^3. Let X_i (i - 1, 2, 3) denote the number of type i containers shipped during a given week. With mu_i = E(X_i) and sigma_i^2 = V(X_j), suppose that the mean values and standard deviations are as follows: mu_1 = 230 mu_2 = 240 mu_3 = 140 sigma_1 - 10 sigma_2 - 13 sigma_3 - 8 (a) Assuming that X_1, X_2, X_3 are independent, calculate the expected value and variance of the total volume shipped. expected value ft^3 variance ft^6 (b) Would your calculations necessarily be correct if the X_j's were not independent? Explain. Both the expected value and the variance would be correct. The expected value would be collect, but the variance would not be correct. Neither the expected value not the variance would be correct.

Explanation / Answer

a) expected value =27*230+125*240+512*140=107890

variance=(27*10)2+(125*13)2+(512*8)2 =19490741

b)the expected value would be correct but the variance would not be correct

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