Dortmund will be hit by cold weather in December. Knowing that cold weather might temper with...

 

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Dortmund will be hit by cold weather in December. Knowing that cold weather might temper with his health, a student considers turning up the heat. If he sticks to his current heater settings, he will stay healthy with probability 0.7 or get sick with probability 0.3. If he turns up the heat, the probabilities change to 0.9 for staying healthy and 0.1 for getting sick. Additional heating costs him 6 €a week. Meanwhile, being sick costs him 20 € a week in lost income and he will stay sick for the rest of the cold period. But if he stays healthy, he can get sick during the next week with the same probabilities. 1. How should our student decide depending on whether the cold period lasts one, two or three weeks? Note, once he made a decision in the beginning, he will stick to it. Formulate the elements of the statistical decision problem. Representing his loss function by a decision tree will be helpful. Dortmund will be hit by cold weather in December. Knowing that cold weather might temper with his health, a student considers turning up the heat. If he sticks to his current heater settings, he will stay healthy with probability 0.7 or get sick with probability 0.3. If he turns up the heat, the probabilities change to 0.9 for staying healthy and 0.1 for getting sick. Additional heating costs him 6 €a week. Meanwhile, being sick costs him 20 € a week in lost income and he will stay sick for the rest of the cold period. But if he stays healthy, he can get sick during the next week with the same probabilities. 1. How should our student decide depending on whether the cold period lasts one, two or three weeks? Note, once he made a decision in the beginning, he will stick to it. Formulate the elements of the statistical decision problem. Representing his loss function by a decision tree will be helpful.

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The problem describes a student who is trying to decide whether to turn up the heat in their apartment during a cold period in December The decision is based on the following factors The cost of heati... View the full answer