# 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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