4.101 Consider a country that imports steel and exports automobiles.

The value per unit of cars exported is measured in units of thousands of dollars per car by the random variable X. The value per unit of steel imported is measured in units of thousands of dollars per ton of steel by the random variable Y. Suppose that the country annually exports 10 cars and imports 5 tons of steel.

Compute the mean and variance of the trade balance, where the trade balance is the total dollars received for all cars exported minus the total dollars spent for all steel imported. The joint probability distribution for the prices of cars and steel is shown in Table 4.11.

Table 4.11 Joint Distribution of Automobile and Steel Prices Price of Automobiles (X)

Price of Steel (Y)

$3

$4

$5

$4 0.10 0.15 0.05

$6 0.10 0.20 0.10

$8 0.05 0.15 0.10