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

Question

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:

(a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X1 + 125X2 + 512X3.]

1 = 200     2 = 260     3 = 120 1 = 9 2 = 12 3 = 6 3 and (3) 5123 LetX (i A shipping company handles containers in three different sizes: (1) 27 (3 x 3 x 3) (2) 125 o2 - Vx), suppose that the mean values and standard deviations are as follows 1,2,3) denote the number of type i containers shipped during a given week with , = E x) and = 200 ,-260 ,-120 (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 variance ft 3 ftG (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain. Neither the expected value nor the variance would be correct. The expected value would not be correct, but the variance would be correct. Both the expected value and the variance would be correct. o The expected value would be correct, but the variance would not be correct

Explanation / Answer

here expected value E(Volume)= 27*200+125*260+512*120=99340

varaince =(27*9)2+(125*12)2+(512*6)2 =11746233

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