1. (100pts) A utility is deciding whether to build a power plant near Sacramento or near Las Vegas. The cost of building a power plant is $10 million near Sacramento and $20 million near Las Vegas. If the company builds near Sacramento, however, and an earthquake occurs near Sacramento during the next 5 years, construction will be terminated and the company will lose $10 million (and will still have to build a power plant near Las Vegas). A priori, the company believes there is a 20% chance that an earthquake will occur near Sacramento during the next 5 years. For $1 million, a geologist can be hired to analyze the fault structure near Sacramento. The geologist will either predict that an earthquake will occur or that an earthquake will not occur. The geologist's past record indicates that she will predict an earthquake on 95% of the occasions for which an earthquake will occur and no earthquake on 90% of the occasions for which an earthquake will not occur. a) Identify the alternatives, states of nature, and payoff table if the geologist is not hired. b) Determine the optimal investment using an expected value criterion; c) Find the expected value of perfect information. d) Find the posterior probabilities of the respective states of nature for each of the geologist's predictions. e) What is the expected value of sample information? Should the utility hire the geologist