You can insure a $50,000 diamond for its total value by paying a yearly premium of D dollars. Let X be the yearly gain to the insurance company resulting from the sale of the policy. If the diamond is not stolen during the year, the insurance company will gain the premium of D dollars. If the diamond is stolen during the year, the insurance company will loose $50,000 minus the premium of D dollars which they have already collected. If the probability of theft in a given year is estimated to be 0.01, what premium should the insurance company charge if it wants the expected gain to equal $1000? [Hint: Start by trying to write the pmf of X using the following table.] p(x) Т

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