A shipping company handles containers in three different siz

A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³, and (3) 512 ft³. Let X_i (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With

_i = E(X_i)

and

_i² = V(X_i),

suppose that the mean values and standard deviations are as follows:

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

a) Expected value

B) Variance

Solution