Please answer all questions

A shipping companyr handles containers In three different sizes: (1) 27 R3 (a x 3 x 31.9) 125 ft3, and (3) 512 ft3. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. Wlm ,u, = 50(1) and 0,2 = lion), suppose that the mean values and standard deviations are as follows: [11:230 p2=240 p3=130 01:10 02:12 133:5 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hit-it: Volume = 27X1 + 125X2 + 512X3.] expected value ta variance E6 (b) Would your calculations necessarily' be correct if the X,'s were not independent? Explain. O The expected value would be correct' but the variance would not be correct. 0 Neither the expected value nor the variance would be correct. 0 Both the expected value and the variance would be correct. 0 The expected value would not be con'ect, but the variance would be correct