A farmer is considering whether or not to plant his crop early. If he plants early, and no late frost occurs, he will gain £3000 in extra harvest. If he plants early and a late frost does occur, he will lose £1000 as the cost of reseeding and will not have any gain in extra harvest. If he doesn't plant early his gain will be £0. The probability of late frost is an unknown parameter 0. (a) Describe the action space and the parameter space. [2] (b) Show that the expected loss function for this decision problem is $ 40000 - 3000 if the farmer plants early, Loa) 10 if the farmer doesn't plant early. [3] (c) The farmer consults the weather report and learns that the prior distribution for the probability of late frost has probability density function 7(0) = 20, 0 € (0,1). Compute the Bayes risk under this prior and find the Bayes optimal action.
