Calculate the expected amount paid
The owner of a grocery shop buys a policy to insure its revenue in the event of catastrophes (e.g. earthquakes, snowstorms etc.) that shut down the business.
The policy pays nothing for the first two catastrophe of the year and 50 000 for each one thereafter, until the end of the year.
The number of catastrophes per year that shut down the business is assumed to have a Poisson distribution with mean 3.
Calculate the expected amount paid to the company under this policy during a one year period.