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 yσx=σy.
(a) if managers believe that costs for both fuels tend to rise and fall together, then they should model x and y as independent.
(b) because the means and sds of these random variables are the same, the random variables x and y are identically distributed.
(c) if told that the costs of heating oil and natural gas are uncorrelated, an analyst should then treat the joint distribution as p(x, y)=p(x)p(y).