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The number of elephants that arrive at a water hole is approximately Poisson distributed with a mean of 4.5 arrivals per hour.

a) Calculate the probability that there would be 2 arrivals in a randomly selected 30 minute period.
b) Calculate the probability that there would be 2 arrivals in a randomly selected 4 hour period.
c) Find the mean and variance of the number of arrivals in any 4 hour period.

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