Exam P Practice Problem 12 – Poisson Model of Hospital Costs

Problem 12A
Suppose that N is the length of stay (in days) in a hospital for gastric bypass surgery. Suppose that N follows a Poisson distribution with a mean of 3 days. The total cost of the hospital stay is 5000N+195N^2 (in dollars). What is the expected cost of the hospital stay for gastric bypass surgery?

Problem 12B
Suppose that N is the number of car accidents in the next year for an individual who just purchased auto insurance. The insurer estimated that N follows a Poisson distribution with E(N^2)=2. What is the probability that this individual will have exactly two accidents in the upcoming year?

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Answers are found below.

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