Question

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 μ_i = E(X_i) and σ_i² = V(X_i),  suppose that the mean values and standard deviations are as follows:

μ1 = 210	μ2 = 260	μ3 = 130
σ1 = 11	σ2 = 12	σ3 = 7

(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 _________ ft^3

variance___________ ft^6

how to get the variance

Answer 1

as the events are independent