Question: In Exercise, is it necessary to assume that the events are independent? What other assumption could be made?
Exercise: In Problem, assume that the grower's loss incurred with the burners would be $17,500 and that the loss incurred with the sprinklers would be $27,500.
a. Find EVPI for the weather conditions (freeze or not).
b. Now assume that the loss incurred with the burners is uniformly distributed between $15,000 and $20,000. Also assume that the loss incurred with the sprinklers is uniformly distributed between $25,000 and $30,000. Now estimate EVPI regarding these losses, under the assumption that a better weather forecast cannot be obtained.
c. Do you think the farmer should put more effort into learning his costs more precisely or should he concentrate on obtaining better weather forecasts?
Problem: An orange grower in Florida faces a dilemma. The weather forecast is for cold weather, and there is a 50% chance that the temperature tonight will be cold enough to freeze and destroy his entire crop, which is worth some $50,000. He can take two possible actions to try to alleviate his loss if the temperature drops. First, he could set burners in the orchard; this would cost $5,000, but he could still expect to incur damage of approximately $15,000 to $20,000. Second, he could set up sprinklers to spray the trees. If the temperature drops, the water would freeze on the fruit and provide some insulation. This method is cheaper ($2,000), but less effective. With the sprinklers he could expect to incur as much as $25,000 to $30,000 of the loss with no protective action. Compare the grower's expected values for the three alternatives he has, considering the various possible loss scenarios for the burners and the sprinklers. Which alternative would you suggest the grower take? Why?