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?