How do you put a Distribution in a Risk Analysis?

In conducting a Probability Risk Analysis or statistical risk Analysis, for example over the actions of nature for a particular period of time and for a particular geographical location, one is expected to put a distribution over all the actions of nature and choose the action that maximizes one's expected utility. My question is, 'How can one do this?' How do you put a distribution over the actions of an opponent? How do you maximize your expected utility? I need a practical demonstration and illustration of this. I shall be grateful if anyone can help. Thank you.


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For example, if historical records show that there are, on average, two potentially damaging earthquakes per year in your area, you could model the time to the next earthquake using the exponential distribution. If the time of day of the earthquake makes a difference to the risk, you could model the time of the earthquake using the uniform distribution. If you know the cost of a large earthquake is between 5 m and 100 m with a most likely figure of 20 m. then maybe the best you can do is to use a triangular distribution until more information is available.