# Thread: Poisson distribution mean and variance

1. ## Poisson distribution mean and variance

Hi,

I'm having trouble understanding the mean and variance for Poisson distribution problems.

I have an example problem where patiens check-in to a clinic according to a Poisson distribution at a average of 7 patients per hour. Given that it takes approximately 10 minutes to see each patient, I need to find the mean and variance of the total service time for patients arriving during a 1h period (it can be assumed that there are enough doctors available so that no patients needs to wait to be seen).

The answers given are E[S]=7 and V[S]=700 but I can't understand why...

If it takes 10 minutes to see each patient, how can the mean of the total service time be less than 10 minutes?

Also, I thought that with Poisson distributions, E[S]=V[S]=lambda, so why are they different here?

Thanks,

Paul

Hi,

I'm having trouble understanding the mean and variance for Poisson distribution problems.

I have an example problem where patiens check-in to a clinic according to a Poisson distribution at a average of 7 patients per hour. Given that it takes approximately 10 minutes to see each patient, I need to find the mean and variance of the total service time for patients arriving during a 1h period (it can be assumed that there are enough doctors available so that no patients needs to wait to be seen).

The answers given are E[S]=7 and V[S]=700 but I can't understand why...

If it takes 10 minutes to see each patient, how can the mean of the total service time be less than 10 minutes?

Also, I thought that with Poisson distributions, E[S]=V[S]=lambda, so why are they different here?

Thanks,

Paul
Let X be the random variable number of patients in one hour and S the random variable service time for patients in a one hour period.

Then S = 10X.

So I'd have thought that E(S) = (10) (7) = 70 minutes (in other words, I'd suggest the given answers contain a typo) and Var(S) = (10^2)(7) = 700 (=> sd(S) = 26.5 minutes).