4.101 Consider a country that imports coal and exports furniture. The value per unit of furniture exported is measured in units of thousands of euros per furniture by the random variable X. The value per unit of coal imported is measured in units of thousands of euros per ton of coal by the random variable Y.

Suppose that the country annually exports 10 pieces of furniture and imports 5 tons of coal. Compute the mean and variance of the trade balance. The joint probability distribution for the prices of furniture and coal is:

Table 4.11 Joint Distribution of Furniture and Coal Prices Price of Furniture (X)

Price of Coal (Y)

€3

€4

€5

€2 0.20 0.00 0.10

€3 0.10 0.15 0.10

€7 0.10 0.20 0.05