Geometric distribution probability of no success at allA town's maintenance department has estimated that the cost of snow removal after a major snowstorm is 100, 000. Historical information suggests that the number of major snowstorms in a winter season follows a geometric distribution for which the probability of no major snowstorms in a season is .4. The town purchases an insurance policy which pays nothing if there is one or less major snowstorms in the season, but the insurance pays 50% of all seasonal snow removal costs for major snowstorms if there are 2 or more major snowstorms. Find the expected payout by the insurer.

Question

Geometric distribution probability of no success at allA town&#039;s maintenance department has estimated that the cost of snow removal after a major snowstorm is 100, 000. Historical information suggests that the number of major snowstorms in a winter season follows a geometric distribution for which the probability of no major snowstorms in a season is .4. The town purchases an insurance policy which pays nothing if there is one or less major snowstorms in the season, but the insurance pays 50% of all seasonal snow removal costs for major snowstorms if there are 2 or more major snowstorms. Find the expected payout by the insurer.

Ben Logan · Accepted Answer

Step 1The way to interpret the geometric distribution here is that success is &quot;the point at which the snowstorms stop&quot;, and p is the probability of the snowstorms stopping. Failure is that there was a snowstorm, therefore making it that the snowstorms did not yet stop.Hence one can use the definition   p  (  1  −  p      )    k  , and at   k  =  0, this would mean that there was no failure because the snowstorms never started.Step 2One can also use the definition   p  (  1  −  p      )          k      −      1       and at   k  =  1, this would mean that on the first attempt, the snowstorm stopped, never starting.

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