(Solved): mean values and standard deviations are as follows: 1=2301=102=2602= ...

mean values and standard deviations are as follows: $$\begin{array}{lll}{?}_1=230& {?}_2=260& {?}_3=110\\ {?}_1=10& {?}_2=12& {?}_3=8\end{array}$$ (a) Assuming that $$X_1,X_2,X_3$$ are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume $$=27X_1+125X_2+512X_3.]$$ $$\begin{array}{ll}\text{ expected value }& {\mathrm{ft}}^3\\ \text{ variance }& {\mathrm{ft}}^6\end{array}$$ (b) Would your calculations necessarily be correct if the $$X_i^{?}$$ 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. The expected value would be correct, but the variance would not be correct. Both the expected value and the variance would be correct. $$x$$