Profit and weather: from past experiences, a wheat farmer ling in manitoba, Cananda finds that his annual profit(in canada dollars) is $80,000 if the summer weather is typical,$50,000 if the weather is unusually dry, and $20,000 if there is a severe storm that destroys much of his crop. weather bureau records indicate that the probability is 0.70 of typical weather, 0.20 of unusually dry weather, and 0.10 of a severe storm. In the next year, let X be the farmer's profit.

Suppose the farmer buys insurance for $3500 that pays him $20,000 in the event of a severe storm that destroys much of the crop and pays nothing otherwise. Find the probability distribution of his profit. Find the mean and summarize the effect of buying this insurance.