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 x up/down. So if we wanted to find the probability of 3 cars passing in 30 minutes, we can’t scale 3/30min up to 6/1hr. We need to keep x as 3 and just scale the mean down to 5.

flashcards

QuestionAnswer
What happens when you need to compare Poisson distribution quantities for different time periods?Scale the mean up or down to the new time period; do not scale the value of x.
If the mean number of cars is 10 per hour, what is the mean for 30 minutes?5 cars per 30 minutes.
When solving a Poisson problem for a different time interval, can you scale the value of x?No, you cannot scale x. Only scale the mean.
To find the probability of 3 cars in 30 minutes when the mean is 10 per hour, what are the correct parameters?Keep x = 3 and scale the mean down to \lambda = 5.