Question Part Submissions Used A shipping company handles containers in three di

Question

Question Part Submissions Used 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:

Mg= 210 2-260 3-100 9-10 2 = 13 3 = 8 (a) Assuming that X1, X2, expected value variance kj are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X1 + 125X2 + 512X3-j 27x,+ 125x2+ 512x ft 3 ft6 (b) Would your calculations necessarily be correct if the X's were not independent? Explain. O The expected value would not be correct, but the variance would be correct. O Neither the expected value nor the variance would be correct. O The expected value would be correct, but the variance would not be correct. O Both the expected value and the variance would be correct.

Explanation / Answer

a)..

Expected value = 27*210 + 125*260 + 512*100

=89370

Variance =272*102 + 1252*132 + 5122*82

=19490741

b).

the expected value would be correct, but the variance would not be correct.

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