申論題

二、(10%) With X₁ denoting the amount of gasoline stocked in a bulk tank at the beginning of a week and X₂ the amount sold during the week, Y = X₁ - X₂ represents the amount left over at the end of the week. Find the mean and variance of Y if the joint function of (X₁, X₂) is given by
f(x₁, x₂) = 3x₁ 0 ≤ x₂ ≤ x₁ ≤ 1
            = 0 elsewhere