Question: Ambulances arrive at the casualty department of a large hospital according to a Poisson process at a rate of one arrival every three minutes. Each ambulance contains one or more patients: \(Y\), the number of patients in an ambulance, has the probability distribution below. (The number of patients in an ambulance is independent of the number in any other ambulance.)

1. Find the mean and variance of the number of patients per ambulance.
2. Find the mean and variance of the number of patients arriving by ambulance:
   during a \(7 \frac{1}{2}\) -hour shift.
3. Find the index of dispersion for this process. What does the value of the index of dispersion tell you about the pattern of arrivals of patient by ambulance?

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