An insurance company wants to design a homeowner's policy for mid-priced homes. From data compiled by the company, it is known that the annual claim amount, X, in thousands of dollars, per homeowner is a random variable with the following probability distribution.

a. Determine the expected annual claim amount per homeowner.
b. How much should the insurance company charge for the annual premium if it wants to average a net profit of $50 per policy?

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0 10 50 100 200 P(X=x)| 0.95 0.045 0.004 0.0009 0.0001