1. If managers believe that costs for both fuels tend to rise and fall together, then they should model X and Y as independent.
2. A negative covariance between X and Y would increase the uncertainty about future costs.
3. Because the means and SDs of these random variables are the same, the random variables X and Y are identically distributed.
4. Because the means and SDs of these random variables are the same, the random variables X and Y are dependent.
5. If the costs of oil and gas are uncorrelated, an analyst should then model the joint distribution as p(x, y) = p(x) p(y).
6. If costs of oil and gas are independent, the complex achieves the minimum variance in total costs by using just oil or just gas.
An office complex leases space to various companies. These leases include energy costs associated with heating during the winter. To anticipate costs in the coming year, the managers developed two random variables X and Y to describe costs for equivalent amounts of heating oil (X) and natural gas (Y) in the coming year. Both X and Y are measured in dollars per Btu of heat produced. The complex uses both fuels for heating, with μx = μy and σx = σy.