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Problem 4. You are responsible for maintaining traffic sensors for a city, and replacing them when they fail. Assume that the number of sensors which need to be replaced each year follows an exponential distribution, with a mean of 8. The manufacturer of these sensors offers two sales packages. Option A costs $50,000 per year; within a given year the first 5 replacement sensors you need are included, and if you need additional sensors, each extra one costs $5,000. Option B costs $70,000 per year and covers the first 10 replacement sensors in a year; additional sensors cost $2,000 each. What are the expected costs of each plan? Which one is lower