Firstly I want to put big disclaimer here. This particular problem is a smaller part of my homework. Since even after discussion with my fellow classmates we are not sure how to handle it we decided to post a question here.
Basically we are supposed to simulate spreading of disease.
Every day every infected person will pick random number of people (possible infected candidates) with Poisson distribution where parameter is 5. Everyone of those selected people (=possible infected candidates) will be infected with probability of 1/2 and at the end of the day the infection takes effect. Next day this particular infected person will be also spreading infection and will again pick random number of people (another possible infected candidates) with Poisson distribution where parameter is again 5. Number of possibly infected candidates and event static whether person will be infected or not are both independent on each other.
Let's suppose on the first day there is only one infected person. I have written a program, that will calculate the number of infected people at the beggining of 8th day (just a simulation).
My question is: after running this simulation 100 times and taking the number from beggining of 8th day as our data, I need to estimate the expected value of infected people using point estimation and 95% interval estimation. How to do this?
What I came up with: I wanted to use $E(\bar{X})=\mu$$=\frac 1n \sum_{i = 1}^{100}x_i$ (where n=100) as my point estimation of expected value. Is this the correct way? The wierd thing about this is that it's just an averagy value.