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# Applications of the Poisson Distribution

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1. Applications of the Poisson Distribution • Let’s consider a random variable N that represents the number of events that occur (in space or time). N has a Poisson distribution if… • Events occur at a constant rate m. • There are no multiple hits (events occurring at exactly the same point in time or space). • Events occur independently.

2. The average number of trucks arriving at a truck depot is 5 per day. What is the probability that fewer than 3 trucks arrive on a given day?

3. m specimens of a rare species of butterfly are found by an avid collector each year. The collector is most interested in the female of the species, but only a fraction p of the specimens collected are female. • What is the probability that i females are collected in a year, (for i = 0, 1, 2)? • What is the probability distribution of the number of females collected in a year?

4. Seeds fall independently in a field at a rate of 0.0023 seeds per square centimeter. What is the probability that between 20 and 26 seeds fall in a particular square meter?