Mary Andrews is organizing a special outdoors show on August 5. The earnings will depend on the weather. If itrains on that day, the show will lose $20,000; if it is sunny, the show is expected to earn $15,000. Historically,the likelihood of rain on any day in early August has been 27%.

Today is July 31, the last day Mary can cancel theshow and only lose her $1,000 deposit on the facilities.

a.Assume Mary will choose her course of action basedon maximizing her expected payoff. What is the most she should be willing to pay today, for a perfectly accurate forecast of the weather on August 5? In other words, what is the EVPI? (5 marks)

Mary can also cancel the show on August 4, but doing so will cost her a late cancellation fee of $5000. The advantage of waiting until then is that she can get the weather forecast for the next day (August 5) from the local news station.

According to station records, the next day weather was forecast to be sunny 90% of the days in early August in past years, and rainy on the other 10%. Thus, there is 90% chance that on August 4, the next day forec

ast for August 5 will be Sunny, and 10% chance the forecast will be Rainy. Symbolically, we can state this

as: P(Next day forecast is Sunny) = 0.90, and P(Next day forecast is Rainy) = 0.10.The predictive ability of these next day weather forecasts has been good, judging from the following posterior probabilities. When next day weather was forecast to be sunny, it turned out sunny 80% of the time, i.e., P(Next day will be Sunny | Next day forecast is Sunny) = 0.80. When the weather was forecast to be rainy, it turned out to be rainy 90% of the time, i.e., P(Next day will be Rainy | Next day forecast is Rainy) = 0.90.

b. Assume, again, that Mary will choose based on maximizing her expected payoff. Should she wait in order to get the next-day local weather forecast (on August 4) before deciding? In other words, what is the EVSI?(10 marks)