Each night different meteorologists give us theprobability
Chapter 4, Problem 4.31(choose chapter or problem)
Each night different meteorologists give us theprobability that it will rain the next day. To judgehow well these people predict, we will score eachof them as follows: If a meteorologist says that itwill rain with probability p, then he or she willreceive a score of1 (1 p)2 if it does rain1 p2 if it does not rainWe will then keep track of scores over a certaintime span and conclude that the meteorologistwith the highest average score is the best predictorof weather. Suppose now that a given meteorologistis aware of our scoring mechanism and wantsto maximize his or her expected score. If this persontruly believes that it will rain tomorrow withprobability p, what value of p should he or sheassert so as to maximize the expected score?
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