A forecaster is indifferent between receiving $1 for sure and any of the following: $8 if tomorrow’s rainfall is greater than 55 mm, $4 if tomorrow’s rainfall is greater than 32 mm, $2 if tomorrow’s rainfall is greater than 12 mm, $1.33 if tomorrow’s rainfall is greater than 5 mm, and $1.14 if tomorrow’s precipitation is greater than 1 mm.
a. What is the median of this individual’s subjective distribution?
b. What would be a consistent 50% central credible interval forecast? A 75% central credible interval forecast?
c. In this forecaster’s view, what is the probability of receiving more than one but no more than 32 mm of precipitation?
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