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_1^2 = V(X_i), suppose that the mean values and standard deviations are as follows: mu_1 = 230 mu_2 = 260 mu_3 =120 sigma_1 = 9 sigma_2 = 12 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 Would your calculations necessarily be correct if the X's 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. Both the expected value and the variance would be correct. The expected value would not be correct, but the variance would be correct.

Explanation / Answer

expected value =27E(X1)+125E(X2)+512E(X3)=27*230+125*260+512*120=100150

variance =272Var(X1)+1252Var(X2)+5122Var(X3) =(27*9)2+(125*12)2+(512*8)2 =19086265

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