A new invention is presented to the scientific consultant of a company. He makes the following assessments: The probability that the invention will work, is p. The profit (gain) of the company, if the invention is applied and it works, is V . The loss of the company, if the invention is applied and does not work, is L. The personal gain of the consultant, if he suggests to apply the invention and the invention works, is v. The personal loss of the consultant in the event that he suggests to apply the invention and the invention does not work, is l. The losses, if the invention is not applied, are negligible, e.g. because neither the company nor the consultant has direct competitors. a) Formulate the situation above as a statistical decision problem. b) Calculate the risk function. c) What should the consultant recommend? When will there be problems with his decision? What could the company do about it?

A new invention is presented to the scientific consultant of a company. He makes the following assess- ments: The probability that the invention will work, is p. The profit (gain) of the company, if the invention is applied and it works, is V. The loss of the company, if the invention is applied and does not work, is L. The personal gain of the consultant, if he suggests to apply the invention and the invention works, is u. The personal loss of the consultant in the event that he suggests to apply the invention and the invention does not work, is l. The losses, if the invention is not applied, are negligible, e.g. because neither the company nor the consultant has direct competitors. a) Formulate the situation above as a statistical decision problem. b) Calculate the risk function. c) What should the consultant recommend? When will there be problems with his decision? What could the company do about it? A new invention is presented to the scientific consultant of a company. He makes the following assess- ments: The probability that the invention will work, is p. The profit (gain) of the company, if the invention is applied and it works, is V. The loss of the company, if the invention is applied and does not work, is L. The personal gain of the consultant, if he suggests to apply the invention and the invention works, is u. The personal loss of the consultant in the event that he suggests to apply the invention and the invention does not work, is l. The losses, if the invention is not applied, are negligible, e.g. because neither the company nor the consultant has direct competitors. a) Formulate the situation above as a statistical decision problem. b) Calculate the risk function. c) What should the consultant recommend? When will there be problems with his decision? What could the company do about it