Poisson mean scaling
When we’re trying to solve problems involving the poisson distribution, we might have a question which involves comparing two things that don’t have the mean set to the same scale.
For example, we might know the mean number of cars that pass through a junction in 1 hour, but we want to know the probability that a certain number of cars pass through in 30 minutes.
To solve these problems, we can just scale the mean up/down to the new, correct, time period.
For our example, if we know that the mean number of cars that pass through a junction in 1 hour is 10, then the mean number of cars that pass through in 30 minutes is just half of that, so an average of 5 cars per 30 minutes.
We can’t scale our value of